Energy-momentum tensor in general conformal field theories have improvement ambiguity and it can affect the argument in deriving c-theorem. While the derivation of Zamolodchikov’s c-theorem is still formally valid with the improved energy-momentum tensor, the behavior of the c-function proposed by Zamolodchikov becomes different. When the theory suffers an IR divergence due to the non-compactness, the c-function can be unbounded and may even show non-monotonicity. We find that one of the three-point function sum rule proposed by Hartman and Mathys motivated by the averaged null energy condition, however, is agnostic about the improvement and gives the (effective) Virasoro central charge, when the IR theory is gapped.

Japan

Nanami Nakamura

Yu Nakayama

c-theorem and improvement in non-compact conformal field theories

<p>Inspired by the possibility of emergent supersymmetry in critical random systems, we study a field theory model with a quartic potential of one superfield, possessing the Parisi-Sourlas supertranslation symmetry. Within perturbative <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>ε</mi></math> expansion, we find nine nontrivial scale-invariant renormalization group fixed points, but only one of them is conformal. We, however, believe scale invariance without conformal invariance cannot occur without a sophisticated mechanism because it predicts the existence of a nonconserved but nonrenormalized vector operator called virial current, whose existence must be nongeneric. We show that the virial current in this model is related to the supercurrent by supertranslation. The supertranslation Ward-Takahashi identity circumvents the genericity argument, explaining its nonrenormalization property.</p>

Parisi-Sourlas Supertranslation and Scale Invariance without Conformal Symmetry

We study the transverse momentum ( $p_T$ ) differential anisotropic flow and flow fluctuation in Pb+Pb collisions at $\sqrt{s_{_{NN}}}$ =5.02 TeV at the LHC. A (3+1)-dimensional CLVisc hydrodynamics framework with fluctuating TRENTO (or AMPT) initial conditions is utilized to simulate the space-time evolution of the quark-gluon plasma (QGP) medium. The effects of shear viscosity and the sub-nucleon structure on anisotropic flow and flow fluctuation are analyzed. Our result shows that shear viscosity tends to suppress both flow coefficients ( ${v_2\{2}\}$ , ${v_2\{4\}}$ , and ${\langle v_2\rangle}$ ) and flow fluctuation ( ${\sigma_{v_2}}$ ) owing to its smearing effect on local density fluctuation. The flow coefficients appear to be insensitive to the sub-nucleon structure, whereas the flow fluctuation ${\sigma_{v_2}}$ tends to be suppressed by the sub-nucleon structure in central collisions but enhanced in peripheral collisions. After taking into account the sub-nucleon structure effect, our numerical result can qualitatively describe the relative flow fluctuations ( ${v_2\{4\}/v_2\{2\}}$ , $F({v_2})$ ) measured by the ALICE Collaboration at the LHC. We further investigate the effects of shear viscosity, sub-nucleon structure, and initial condition model on the flow angle and flow magnitude decorrelations ( ${A_2^f}$ , ${M_2^f}$ ) using the four-particle correlation method. We find that the flow decorrelation effect is typically stronger in central collisions than in peripheral collisions. The flow angle decorrelation is found to be insensitive to the shear viscosity and sub-nucleon structure, whereas the flow magnitude decorrelation shows quite different behaviors when using the TRENTO and AMPT initial condition models. Our study sheds light on the anisotropic flow, transport properties, and initial structure of the QGP created in high-energy nuclear collisions.

China

Germany

Jie Zhu

Canada

Xiang-Yu Wu

Guang-You Qin

Anisotropic flow, flow fluctuation, and flow decorrelation in relativistic heavy-ion collisions: the roles of sub-nucleon structure and shear viscosity * Supported in part by the Natural Science Foundation of China (12225503, 11890710, 11890711, 11935007). Zhu Jie is supported in part by the China Scholarship Council (202306770009). Wu Xiang-Yu is supported in part by the National Science Foundation within the framework of the JETSCAPE collaboration (OAC-2004571) and in part by the Natural Sciences and Engineering Research Council of Canada. Some of the calculations were performed in the Nuclear Science Computing Center at Central China Normal University (NSC$^{3}$), Wuhan, Hubei, China.

Based on the study of non-invertible symmetries, we propose there exist infinitely many new renormalization group flows between Virasoro minimal models   <math> <mi>M</mi> </math>  $$ \mathcal{M} $$ (kq + I, q) →   <math> <mi>M</mi> </math>  $$ \mathcal{M} $$ (kq – I, q) induced by ϕ (1,2k+1). They vastly generalize the previously proposed ones k = I = 1 by Zamolodchikov, k = 1, I &gt; 1 by Ahn and Lässig, and k = 2 by Dorey et al. All the other ℤ 2 preserving renormalization group flows sporadically known in the literature (e.g.   <math> <mi>M</mi> </math>  $$ \mathcal{M} $$ (10, 3) →   <math> <mi>M</mi> </math>  $$ \mathcal{M} $$ (8, 3) studied by Klebanov et al) fall into our proposal (e.g. k = 3, I = 1). We claim our new flows give a complete understanding of the renormalization group flows between Virasoro minimal models that preserve a modular tensor category with the SU(2) q−2 fusion ring.

Takahiro Tanaka

Infinitely many new renormalization group flows between Virasoro minimal models from non-invertible symmetries

A dipolar fixed point introduced by Aharony and Fisher is a physical example of interacting scale-invariant but nonconformal field theories. We find that the perturbative critical exponents computed in <math><mi>ε</mi></math> expansions violate the conformal bootstrap bound. We formulate the functional renormalization group equations à la Wetterich and Polchinski to study the fixed point. We present some results in three dimensions within (uncontrolled) local potential approximations (with or without perturbative anomalous dimensions).

Functional renormalization group approach to dipolar fixed point which is scale invariant but nonconformal

In the Einstein-Maxwell-charged scalar system with a negative cosmological constant in arbitrary dimensions higher than three, there exists a horizonless charged soliton solution, which we construct explicitly for an arbitrary mass of the scalar in perturbative series in small charge. We find that the stability of the soliton is determined by the validity of the AdS weak gravity conjecture. The existence of a stable soliton might endanger the convexity of the (free) energy as a function of the charge because the phase transition between the soliton and the extremal Reissner-Nordstrom black hole would be discontinuous. We, however, argue that the existence of the hairy black hole solution circumvents the violation of convexity. The thermodynamic properties of the hairy black hole show that the phase transition becomes continuous irrespective of whether the AdS weak gravity conjecture holds. When it holds, the phase transition occurs between the soliton and the hairy black hole, and when it is violated, the phase transition occurs between the extremal Reissner-Nordstrom black hole and the hairy black hole.

Takaaki Ishii

Convexity restoration from hairy black hole in Einstein-Maxwell-charged scalar system in AdS

We study a higher group analog of the Weyl symmetry in four-dimensional quantum field theories. A typical example is that the modified transformation of the 2-form background gauge field replaces the operator-valued Weyl anomaly associated with gauging the 0-form global symmetry. It is analogous to the 2-group global symmetry where the modified transformation of the 2-form background gauge field replaces the operator-valued chiral anomaly associated with gauging the 0-form symmetry. The physical origin of the higher group Weyl symmetry is that under the renormalization group flow, the conserved current mixes with the electromagnetic current that couples with the dynamical gauge field. We can express these effects in the local renormalization group equations in a unified manner.

Higher group Weyl symmetry

We investigate the fate of the non-supersymmetric Gross-Neveu-Yukawa fixed point found by Fei et al. in 4 − ϵ dimensions with a two-component Majorana fermion continued to two dimensions. Assuming that it is a fermionic minimal model which possesses a chiral ℤ2 symmetry (in addition to fermion number parity) and just two relevant singlet operators, we can zero in on four candidates. Assuming further that the least relevant deformation leads to the supersymmetric Gross-Neveu-Yukawa fixed point (i.e. fermionic tricritical Ising model), we can rule out two of them by matching the spin contents of the preserved topological defect lines. The final candidates are the fermionic (11, 4) minimal model if it is non-unitary, and the fermionic (E 6 , A 10) minimal model if it is unitary. If we further use a constraint from the double braiding relation proposed by one of the authors, the former scenario is preferable.

Ken Kikuchi

The fate of non-supersymmetric Gross-Neveu-Yukawa fixed point in two dimensions

We construct a purely fermionic system with spontaneously broken supersymmetry that shares the common feature with a fracton phase of matter. Our model is gapless due to the Nambu-Goldstone mechanism. It shows a ground-state degeneracy with the “Area-law” entropy due to fermionic subsystem symmetries. In the strongly coupled limit, it becomes a variant of the Nicolai model, and we conjecture that the ground-state degeneracy shows the “Volume-law” entropy. Gauging the fermionic subsystem symmetry has an t’Hooft anomaly by itself, but the would-be gauged theory may possess a fermionic defect that is immobile in certain spatial directions.

Hosho Katsura

Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries

We show that <math><mi>C</mi><mi>P</mi></math>-violating Weyl anomaly induces a supersymmetry anomaly in the formulation of superconformal supergravity as is observed in <math><mi>C</mi><mi>P</mi></math>-preserving cases. This supersymmetry anomaly can be removed in the old minimal supergravity by adding suitable local counterterms, and it becomes a consistent theory.