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2608.13557
2 days ago

Localised Horizons and Holographic Thermodynamics: Supercooling in the 1/D Expansion

Prateek Agrawal, Gaurang Ramakant Kane, Vazha Loladze

In holography, four-dimensional confining gauge theories are often modelled by five-dimensional Einstein--scalar gravity by choosing a specific form of the scalar potential. In a large class of non-conformal theories, we show that a predictive structure emerges for the thermal confinement transition by generalising the gravitational dual to D+1D+1D+1 dimensions and using a 1/D1/D1/D

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expansion. These results are independent of the details of the scalar potential, hinting towards universality. The black brane geometry dual to the deconfined phase can be analytically constructed due to its effects being localised near the horizon at leading order. The solution does not exist below a minimal temperature
TminT_{\rm min}Tmin​
and the maximum possible supercooling in the transition
εsc=1−Tmin/Tcε_{\rm sc} = 1-T_{\rm min}/T_{\rm c}εsc​=1−Tmin​/Tc​
is generically suppressed by a factor of
1/D21/D^21/D2
. Remarkably, the maximum supercooling at the leading order is set by the speed of sound in the deconfined phase of the gauge theory at the critical temperature,
εsc=cs2(Tc)/2ε_{\rm sc}=c_s^2(T_{\rm c})/2εsc​=cs2​(Tc​)/2
. These predictions agree with explicit calculations in an exponential superpotential, improved holography, and the thermal transition in
N=4\mathcal{N}=4N=4
super Yang--Mills on a sphere.
TheoryLatticePhenomenology
2608.13542
2 days ago

Effective field theory of quasi-hydrodynamics from kinetic theory

Lorenzo Gavassino

Quasi-hydrodynamics describes systems with quasi-conserved degrees of freedom, namely observables that relax on timescales that are finite but parametrically longer than microscopic relaxation times. Examples include kinetic chemistry and linear viscoelasticity. Here, we develop a rigorous effective-field-theory framework for linear quasi-hydrodynamics from kinetic-type theories. Starting from any linearized, causal kinetic-like theory endowed with slow degrees of freedom, we show that the exact dynamics of conserved and quasi-conserved observables admits a systematic expansion in the fast relaxation timescale. At zeroth order, the resulting equations form a causal, symmetric-hyperbolic theory belonging to the appropriate transient-hydrodynamic universality class, establishing Israel-Stewart-like dynamics as the universal description of slow relaxation modes. Higher-order corrections can be computed systematically and inherit universal symmetry, Onsager, positivity, and causality constraints from the underlying microscopic theory.

Nuclear TheoryTheoryMathematical Physics
2608.13529
2 days ago

Vector Perturbations in Ghost-Free Quasidilaton Massive Gravity

Ekapob Kulchoakrungsun, Daris Samart

We study transverse vector perturbations in ghost-free extended quasidilaton massive gravity without a quasidilaton kinetic term, in the presence of minimal matter. In vacuum, we recover the known result that the kinetic coefficient KVK_VKV​ of the gravitational vector modes vanishes on the self-accelerating branch J=0J=0J=0, so those modes are infinitely strongly coupled at linear order. We then add a canonical scalar field and a single Abelian vector (Maxwell or Proca). After integrating out the auxiliary shift, we find the same KVK_VKV​ as in vacuum. The scalar matter has no transverse perturbation; it enters the unsimplified shift constraint, but those terms cancel once the Friedmann equation is used. A Maxwell or Proca field with vanishing isotropic background does not mix with the gravitational vectors at quadratic order. Minimal matter therefore leaves KV=0K_V=0KV​=0 on Branch II. We do not claim that the modes are absent from the nonlinear theory. We do conclude that ordinary minimal matter is not enough to make the vector sector perturbatively healthy on this branch. If we need healthy gravitational vector modes at the linear level, Branch I is the branch to use.

General Relativity and Quantum CosmologyCosmology and Nongalactic AstrophysicsTheory
2608.13498
2 days ago

Quadratic effective energy--momentum tensor on uniform-density hypersurfaces during slow-roll inflation

Inyong Cho

We investigate the quadratic-order effective energy--momentum tensor (2EMT) of scalar cosmological perturbations on uniform-density hypersurfaces during slow-roll inflation. The 2EMT is constructed from terms quadratic in the linear metric and inflaton perturbations, and is therefore a gauge-fixed effective source rather than a gauge-invariant observable. We impose the complete scalar gauge conditions δρ=0δρ=0δρ=0 and E=0E=0E=0, express all perturbations in terms of the Bardeen potential ΨΨΨ, and evaluate the Fourier-space 2EMT in the long- and short-wavelength domains. We distinguish the ``strict'' infrared and ultraviolet limits from the ``intermediate'' regimes. The uniform-density and comoving results agree in the strict infrared limit. In the intermediate infrared regime, the dominant leading order remains the same, while explicit finite-gradient corrections distinguish the two gauges. In the ultraviolet, the 2EMT is enhanced by 1/ε1/ε1/ε due to the slowly varying matter clock, ρ0′∝ερ_0'\proptoερ0′​∝ε, and the leading uniform-density 2EMT terms exhibit an additional enhancement by 1/σ221/σ_2^21/σ22​ (σ2≡H/k)(σ_2\equiv \cal{H}/k)(σ2​≡H/k) from the Laplacian term. The intermediate ultraviolet expansion makes the subleading gradient hierarchy explicit without changing the leading terms. We compare these results with newly recalculated longitudinal, spatially-flat, and comoving expressions, displayed in a more explicit form than in the earlier analysis. The comparison shows that the gauge dependence is structured: uniform-density and comoving slicings coincide for adiabatic super-Hubble modes, whereas the longitudinal and spatially-flat gauges are slow-roll suppressed in the strict infrared and become gradient dominated in the intermediate infrared.

General Relativity and Quantum CosmologyTheory
2608.13488
2 days ago

Higher-Order Analytical Expansion of Thawing Dark Energy with an Exponential Potential

Naoto Maki, Kazunori Kohri

Motivated by recent DESI results suggesting dynamical dark energy, we investigate the thawing scenario in quintessence with an exponential potential, V=V0e−λφ/mplV=V_0e^{-λφ/m_{\mathrm{pl}}}V=V0​e−λφ/mpl​, by analytically expanding the deviation of the equation of state parameter wφw_φwφ​ from −1-1−1 in powers of λλλ. In addition to the previously known leading-order result at O(λ2)O(λ^2)O(λ2), we derive the O(λ4)O(λ^4)O(λ4) correction as a function of the density parameter ΩφΩ_φΩφ​. We show that a consistent determination of the redshift dependence of wφw_φwφ​ through O(λ4)O(λ^4)O(λ4) requires corrections to the background expansion. We obtain the required correction by expanding ΩφΩ_φΩφ​ in powers of λλλ around its ΛCDMΛ\mathrm{CDM}ΛCDM value. Comparison with numerical solutions demonstrates that the O(λ4)O(λ^4)O(λ4) expansion provides a more accurate approximation than the leading-order result. Our analytical approximation, which consistently incorporates the O(λ4)O(λ^4)O(λ4) correction, will provide a potentially useful tool for distinguishing the exponential quintessence model from other dark energy models in future observations.

Cosmology and Nongalactic AstrophysicsGeneral Relativity and Quantum CosmologyPhenomenology
2608.13475
2 days ago

Hidden Dyson Universality in Inverse-Spectral Geometry

Momo Hayashi, Kazumitsu Sakai

Dyson universality typically manifests itself in local eigenvalue statistics. Here we show that its signature survives a nonlinear inverse-spectral reconstruction and reappears in the matrix geometry of the reconstructed operator. Using a dressing transformation, we map each unfolded spectrum to a deformation f(x)f(x)f(x) of a fixed harmonic oscillator and represent it in the common oscillator basis by F_mn= m|f|n. We resolve the matrix-element weight into shells of fixed distance d=∣m−n∣d=|m-n|d=∣m−n∣, corresponding to the energy-transfer channels of the reference oscillator, and characterize the resulting distribution by distance-shell moments. Independently calibrated on Gaussian βββ-ensembles, these moments vary smoothly with βββ and distinguish the GOE, GUE, and GSE. With this calibration fixed, applying the same diagnostic to the nontrivial zeros of the Riemann zeta function places the reconstructed operators in the GUE sector. Thus, the GUE character of the zeros is recovered not through direct statistics of the input levels, but from the distance-resolved geometry of the reconstructed operator.

Mathematical PhysicsStatistical MechanicsTheory
2608.13462
2 days ago

Aperiodicity is sufficient for macroscopic thermalization

Amit Vikram

We identify a general mechanism for the finite-time thermalization of macroscopic observables, such as coarse-grained charge densities, in terms of elementary forms of the quantum dynamics of initial states: (1) aperiodicity, which provides a computable measure of (2) a dynamical partially ergodic exploration of the Hilbert space. Specifically, this mechanism predicts the equilibration of all (concentrated) macroscopic observables, in almost all states in an initial ensemble and almost all times within finite and longer intervals, given only the observable-independent information that the return probability of the ensemble of initial states is small over a finite time range. As a special case, it also accesses standard results on equilibration over infinitely long times in terms of (stronger versions of) the effective dimension of initial state delocalization in the energy eigenbasis. Our results incorporate macroscopic thermalization into the domain of operational quantum statistical mechanics, recently developed to provide finitely computable criteria for microscopic thermalization. We discuss an overall characterization of this approach as establishing connections between (1) the decay of a (theoretically or experimentally) computable probe indicating memorylessness, (2) a fundamental invariant mechanism in terms of the alignment of observables or states in the Hilbert space, and (3) predicting different natural forms of (classical and) quantum thermalization, most of which rigorously recover conventional eigenstate-based descriptions of infinite-time thermalization as a special case but provide stronger accessible predictions over finite observation times in the thermodynamic limit.

Quantum PhysicsStatistical MechanicsTheory
2608.13449
2 days ago

Spectral Localization Principle for Entanglement Harvesting

Hao Xu

We propose a unified physical principle for entanglement harvesting: the entanglement that two localized detectors can extract from a quantum field is determined solely by how localized the field's effective spectral density is. We demonstrate this in an analytically solvable model of two qubits coupled to a leaky single-mode cavity, which in turn couples to a continuous electromagnetic bath, and derive the maximum harvestable concurrence in closed form, Cmax⁡(Q)=2e−π/(2Q)(1+e−π/(2Q))/(1+3e−π/Q)\mathcal{C}_{\max}(Q)=2e^{-π/(2Q)}(1+e^{-π/(2Q)})/(1+3e^{-π/Q})Cmax​(Q)=2e−π/(2Q)(1+e−π/(2Q))/(1+3e−π/Q), where Q≡∣Δ∣/κQ\equiv|Δ|/κQ≡∣Δ∣/κ is the ratio of the qubit-cavity detuning ΔΔΔ to the cavity linewidth κκκ. In the high-QQQ limit, Cmax⁡≃1−π2/(16Q2)\mathcal{C}_{\max}\simeq1-π^{2}/(16Q^{2})Cmax​≃1−π2/(16Q2), so the entanglement is robust against cavity loss; in the low-QQQ limit it decays exponentially to zero, consistent with the irreversible-reservoir character of a continuous field, where maximal entanglement is unattainable. Since QQQ is proportional to the inverse participation ratio (IPR) of the effective spectral density, it is the single dimensionless parameter governing the crossover from deterministic gate-based entanglement (Q→∞Q\to\inftyQ→∞) to vacuum harvesting (Q→0Q\to0Q→0). Our framework operationalizes the Reeh-Schlieder theorem by quantifying the fraction of vacuum correlations accessible to localized detectors. It also reveals a formal correspondence of the maximal concurrence with the IPR, analogous to the conductivity-participation-ratio relation in Anderson localization. The predicted Cmax⁡(Q)\mathcal{C}_{\max}(Q)Cmax​(Q) curve is, in principle, directly observable in superconducting circuit QED experiments.

Quantum PhysicsGeneral Relativity and Quantum CosmologyTheory
2608.13378
2 days ago

Quantum-Corrected Thermodynamics and Phase Structure of AdS Euler-Heisenberg Black Hole

Siddhartha Sankar Borah, Dhruba Jyoti Gogoi, Kalyan Bhuyan

We investigate the thermodynamic behaviour of an AdS black hole arising from nonlinear electrodynamics-corrected gravity, incorporating quantum effects through thermal fluctuations. From the Einstein--Euler--Heisenberg framework, we consider the modified black hole solution and analyse its thermodynamic properties in the extended phase space. Logarithmic and inverse-area corrections to the entropy are obtained, leading to modified expressions for enthalpy, internal energy, Helmholtz free energy and Gibbs free energy. The corrected specific heat exhibits multiple divergences and sign changes, signalling genuine second-order phase transitions and revealing a quantum-stabilized microscopic phase followed by universal macroscopic instability. Our results demonstrate that thermal fluctuations qualitatively restructure the thermodynamic phase space and highlight the dominant role of quantum corrections in governing the black hole stability.

General Relativity and Quantum CosmologyTheory
2608.13319
2 days ago

Holographic Renormalization for String-Derived Lovelock--Horndeski Theory

Tianhao Wu

String-derived higher-curvature scalar--tensor gravities encode microscopic coupling data in boundary response, raising the question of whether holographic observables can reconstruct the underlying higher-dimensional parameters. We answer this question for the five-dimensional string-derived Lovelock--Horndeski (SDLH) theory on its exact linear-dilaton asymptotically locally AdS branch, constructing the renormalized generating functional for an arbitrary boundary metric and spacetime-dependent scalar source. A boundary-covariant radial hierarchy unifies the variational problem, local backreaction, logarithmic obstruction, finite one-point functions, and Ward identities. Two response determinants organize the recursion, resonant obstructions, and metric--scalar mixing. The Weyl anomaly condenses into an Euler density, a Weyl-squared density, and a single curvature--scalar square whose paired variations generate the metric and scalar obstructions. The resulting renormalized functional carries string-selected coupling data into boundary geometry, operator response, anomaly coefficients, and a calculable interface with gravitational observables. On the regular branch, four scalar-normalization-invariant holographic combinations admit a global rational inverse to the continuous reduced couplings. At fixed compactification dimension the map has maximal rank, while the curvature-anomaly sum reconstructs the higher-dimensional Gauss--Bonnet coefficient without sign ambiguity. Holographic response thus provides an explicit, overdetermined boundary fingerprint of the underlying string reduction.

TheoryGeneral Relativity and Quantum Cosmology
2608.13301
2 days ago

Frame-dependency of the confinement temperature in a strongly-coupled plasma under rotation: a holographic description

Nelson R. F. Braga, Alexsandre L. Ferreira

Recently, it was demonstrated that the disagreement between lattice calculations and holographic models, regarding rotational effects in the quark-gluon plasma (QGP), occurs due to different choices of reference frames. While a static observer measures a confinement temperature that decreases with rotation, one in a co-rotating frame finds the opposite behavior. Both results are correct, and a comprehension of the frame-dependency of the critical temperature is a significant step in the description of the QGP under rotation. In this article, we generalize this previous holographic result by describing the plasma through the most general Myers-Perry black hole solution. This breaks the spherical symmetry present in the equal angular momentum case, considered before. As a consequence, the local temperature measured by a co-rotating observer has a non-trivial angular dependence: it can decrease, increase or even behave non-monotonically when rotational velocity increases.

TheoryPhenomenology
2608.13300
2 days ago

3d N=\mathcal{N}=N= 4 rank-0 SCFT from punctured lens space

Sungjoon Kim

Gang-Kim-Stubbs theory Tn\mathcal{T}_nTn​ --- a pioneering 3d bulk description of M(2n+3,2)M(2n+3,2)M(2n+3,2) Virasoro minimal model as N=4\mathcal{N}=4N=4 rank-0 superconformal field theory upon topological A-twist --- is derived from the compactification of a pair of parallel M5-branes on lens space L(2n+3,2)L(2n+3,2)L(2n+3,2) with a single vertex removed. From this perspective, we propose a family of 3d N=2\mathcal{N}=2N=2 abelian gauge theories arising from the punctured L(2n+3,1)L(2n+3,1)L(2n+3,1) lens space whose infrared phases realize the unitary member in the Galois orbit of M(2n+3,2)M(2n+3,2)M(2n+3,2) modular tensor category. We also conjecture self-mirror rank-0 fixed points from amphichirality condition of the lens space.

Theory
2608.13246
2 days ago

Phase transition from eigenstate thermalization: forbidden singularity and instanton proliferation via AGT correspondence

Yongjiang Xu, Weixin Sun, Chushun Tian +1

In theoretical physics, finding connections between problems that appear in distinct contexts is an important way to leapfrog progresses, often by illuminating deep aspects that may otherwise seem obscure. In this paper, we consider in 2d CFTs the phenomenon of forbidden singularities in auto-correlation functions -- a key signature of eigenstate thermalization. We show that they correspond to phase transitions in the context of eigenstates. The connection is made explicit by utilizing the AGT correspondence, which relates eigenstate auto-correlations to the Nekrasov partition functions describing an instanton gas of the N=2\mathcal{N}=2N=2 SUSY gauge theories. We show that by taking the counter-part of the heavy-light limit, two phases emerge for the instanton gas. They are dominated by configurations represented by string-like Young tableaux with distinct structures and thermodynamic properties, which bare resemblance to the confined and the deconfined phases. A phase transition occurs as instantons proliferate from one side, in a manner that mimics the Lee-Yang theory. We work out the critical fugacity and find it corresponding exactly to the forbidden singularity.

Theory
2608.13174
2 days ago

Lee-Yang paradigm of phase transition in eigenstate thermalized systems

Yongjiang Xu, Weixin Sun, Chushun Tian +1

As phase transitions in isolated quantum systems remain elusive, here we show how a thermodynamic-like phase transition, falling into the Lee-Yang paradigm, can arise in systems displaying eigenstate thermalization. Specifically, we show that in holographic conformal field theories, the eigenstate expectation of the auto-correlation function can be mapped to the partition function Zgauge(z){\cal Z}_{gauge}(z)Zgauge​(z) of a virtual interacting instanton gas, with the conformal mapping of the imaginary time: z=1−e−τz=1-e^{-τ}z=1−e−τ and the central charge ccc mimicking the instanton fugacity and volume, respectively. We find that akin to the Lee-Yang paradigm, for c→∞c\to\inftyc→∞ a pair of complex conjugate zeros of Zgauge(z){\cal Z}_{gauge}(z)Zgauge​(z) move to the real axis located at the famous forbidden singularity. Passing through the singularity the system transits from the low- to high-fugacity phase, accompanied by dramatic changes in scaling behaviors of the free energy and dominant microscopic configurations. Our findings indicate that physics of phase transitions from eigenstate thermalization is very rich.

Theory
2608.13155
2 days ago

Single-Variable Solutions in Supergravity

W. A. Sabra, R. Slim

We construct four families of spacetime metrics depending on a single variable for a broad class of DDD-dimensional gravitational theories coupled to scalar and Abelian gauge fields. As applications of the general formalism, we derive one-variable solutions of ungauged N=2\mathcal{N}=2N=2, D=4D=4D=4 supergravity coupled to vector multiplets. We also obtain explicit solutions for a consistent truncation of N=8\mathcal{N}=8N=8, D=4D=4D=4 supergravity, as well as for theories whose scalar fields parametrize the symmetric coset manifolds SL(N,R)/SO(N,R)SL(N,\mathbb{R})/SO(N,\mathbb{R})SL(N,R)/SO(N,R). In all cases, the geometry of the scalar manifold plays a central role in determining the structure of the resulting solutions with nontrivial scalar and gauge field configurations.

TheoryGeneral Relativity and Quantum Cosmology
2608.13117
2 days ago

Exact Evaluation of Lattice-Regularized Scalar Field Vacuum Amplitude via Site Permutations

Vadim Asnin

A novel approach to a computation of vacuum amplitude for a single scalar field in any number of dimensions with arbitrary potential on a lattice is proposed. The computation involves symmetrization of kinetic exponential factor in the path integral over all permutations of lattice sites and Waring decomposition of the symmetrized expression.

Theory
2608.13105
2 days ago

Limits of the inverse scattering problem

Matvei Fedin, Kirill Gubarev, Andrey Morozov

The main goal of tomography is the reconstruction of density function out of its line integrals (integral measurements of this density along x-ray lines). Such construction is possible and known as inverse x-ray/Radon transformations. We are interested in generalization of this problem to the case of particles. For this we need to limit the speed of these particles, otherwise the problem is reduced to the previous one. The question we discuss in this paper is how low can this speed be depending on the parameters of the studied potential. We study this problem using simple theoretical examples and Machine Learning pipeline to restore the potential.

TheoryMathematical Physics
2608.12883
2 days ago

Topological properties around the Roberge-Weiss transition in Nf=2+1+1N_f = 2 + 1 + 1Nf​=2+1+1 QCD

Massimo D'Elia, Fabio Siliberto, Kevin Zambello

We investigate the topological properties of QCD across the finite temperature Roberge-Weiss transition, which is found for particular values of the imaginary baryon chemical potential. Our study is conducted for Nf=2+1+1N_f = 2+1+1Nf​=2+1+1 QCD with physical quark masses, discretized via stout improved staggered fermions and considering mostly two different values of the compactifed dimension, Nt=8N_t = 8Nt​=8

LatticeTheory
2608.12850
2 days ago

D4-branes wrapped on topological disks from matter-coupled F(4) gauged supergravity

Patharadanai Nuchino, Parinya Karndumri

We study a number of supersymmetric AdS4×ΣAdS_4\times ΣAdS4​×Σ solutions with ΣΣΣ being a topological disk with non-trivial U(1)U(1)U(1) holonomy on the boundary or a ``half-spindle'' from matter-coupled F(4)F(4)F(4) gauged supergravity. The gauged supergravity is coupled to three vector multiplets with SO(3)×SO(3)SO(3)\times SO(3)SO(3)×SO(3) gauge group. The resulting solutions preserve eight supercharges and SO(2)×SO(2)SO(2)\times SO(2)SO(2)×SO(2) or SO(2)diagSO(2)_{\text{diag}}SO(2)diag​ symmetries and are expected to be dual to N=2N=2N=2 SCFTs in three dimensions arising from compactifications of five-dimensional N=2N=2N=2 SCFT on a half-spindle. All of the solutions lie within the U(1)×U(1)U(1)\times U(1)U(1)×U(1) subsector of the matter-coupled F(4)F(4)F(4) gauged supergravity that can be embedded in massive type IIA theory. After uplifted to ten dimensions, the solutions can be interpreted as a system of D4-D8-branes wrapped on ΣΣΣ. Some of the solutions are asymptotic to a locally AdS6AdS_6AdS6​ geometry and can be identified as codimension-2 conformal defects within the N=2N=2N=2 SCFT in five dimensions. For these solutions, the circle inside ΣΣΣ decompactifies in the AdS6AdS_6AdS6​ limit rendering the holographic free energy infinite. There also exist solutions with finite free energy in the dual three-dimensional SCFTs. In addition, we show that the results both extend the previously known solutions and provide a novel class of solutions.

Theory
2608.12819
2 days ago

Waterfall-modulated ααα-attractors

Renata Kallosh, Andrei Linde, Yusuke Yamada

Hybrid ααα-attractor models Kallosh:2022ggf can have significantly greater values of nsn_{s}ns​ and smaller rrr, while preserving the relation r≅3α(1−ns)2r\cong 3α(1-n_s)^2r≅3α(1−ns​)2, which is valid for exponential T- and E-models at large values of the inflaton field. Here we study single-field ααα-attractors with features inspired by hybrid models: one can uplift the potential, and one can also have a waterfall regime that leads to a premature termination of inflation near the critical point φc\varphi_cφc​. This allows one to increase the effective number of e-foldings NcN_cNc​ in formulas like ns≃1−2Ncn_s\simeq 1-{2\over N_c}ns​≃1−Nc​2​, r≃12αNc2r\simeq {12 α\over N_c^2}r≃Nc2​12α​. By changing the waterfall's steepness and location, one can continuously move the predictions along the curves with r≅3α(1−ns)2r\cong 3α(1-n_s)^2r≅3α(1−ns​)2 as nsn_sns​ increases and rrr decreases. We also study the effect of waterfall insertions and uplift on nsn_sns​ in quintessential ααα-attractors that describe inflation and dynamical dark energy.

Cosmology and Nongalactic AstrophysicsGeneral Relativity and Quantum CosmologyTheory
and
Nt=10N_t = 10Nt​=10
. Results for
TRWT_{RW}TRW​
and for the associated universality class are consistent with those found in the
Nf=2+1N_f = 2 + 1Nf​=2+1
case with a slightly different discretization. The topological susceptibility appears to be practically constant for
T≲TRWT \lesssim T_{RW}T≲TRW​
, then rapidly decaying for higher temperatures. The analysis of the fourth order cumulant of the topological charge distribution,
b2b_2b2​
, reveals that it is compatible with the prediction of the Dilute Instanton Gas Approximation right after
TRWT_{RW}TRW​
, showing thus a sharp transition, which is more similar to what observed in pure gauge theories rather than to full QCD along the standard thermal line, where instead a slower transition was observed in previous studies.