The multicritical generalizations of the Lee-Yang universality class arise as renormalization-group fixed points of scalar field theories with complex $\textit{iφ}$ interaction, $\textit{n}$ ∈ ℕ, just below their upper critical dimension. It has been recently conjectured that their continuation to two dimensions corresponds to the non-unitary conformal minimal models ℳ(2$\textit{,}$ 2$\textit{n}$ + 3). Motivated by that, we revisit the functional renormalization group approach to complex 𝒫𝒯-symmetric scalar field theories in the Local Potential Approximation, without or with wavefunction renormalization (LPA and LPA’ respectively), aiming to explore the fate of the $\textit{iφ}$ theories from their upper critical dimension to two dimensions. The $\textit{iφ}$ fixed points are identified using a perturbative expansion of the functional fixed-point equation near their upper critical dimensions, and they are followed to lower dimensions by numerical integration of the full equation. A peculiar feature of the complex 𝒫𝒯-symmetric potentials is that the fixed points are characterized by real but negative anomalous dimensions $\textit{η}$, and in low dimension $\textit{d}$, this can lead to a change of sign of the scaling dimensions ∆ = ($\textit{d}$ − 2 + $\textit{η}$)$\textit{/}$2, thus requiring a novel analysis of the analytical properties of the functional fixed-point equations. We are able to follow the Lee-Yang universality class ($\textit{n}$ = 1) down to two dimensions, and numerically determine the scaling dimension of the fundamental field as a function of $\textit{d}$. On the other hand, within the LPA’, multicritical Lee-Yang fixed points with $\textit{n >}$ 1 cannot be continued to $\textit{d}$ = 2 due to the existence of unexpected non-perturbative fixed points that annihilate with the $\textit{iφ}$ fixed points.

France

Dario Benedetti

Fanny Eustachon

Italy

Omar Zanusso

Critical and multicritical Lee-Yang fixed points in the local potential approximation

We analyze the behavior of holographic subregion complexity (HSC) and holographic fidelity susceptibility (HFS) in noncommutative Yang-Mills theory. The emergence of a minimum length scale, dictated by the degree of noncommutativity, induces a behavioral transition in the HSC and establishes a lower bound. In the large noncommutativity regime, the qualitative features of the complexity deviate significantly from the commutative case. The HFS is shown to provide an effective measure of the degree of noncommutativity. Although the HSC generally satisfies strong subadditivity, this property fails abruptly when the subregion size approaches the minimum length scale. At finite temperature, the long-range behavior of the HSC is modified, and its lower bound scales positively with temperature. Furthermore, temperature enhances the sensitivity of the fidelity susceptibility to the degree of noncommutativity. Within the AdS soliton background, a competition between connected and disconnected configurations arises in the HSC, signaling a phase-transition-like behavior. Finally, the compactification scale is found to diminish the sensitivity of the HFS to the degree of noncommutativity.

Japan

Tadahito Nakajima

Holographic subregion complexity and fidelity susceptibility in noncommutative Yang-Mills theory

We study the resurgent structure of the topological string dual to 2d U($\textit{N}$) Yang-Mills on torus. We find closed form formulas for instanton amplitudes up to arbitrarily high instanton orders, based on which we propose the non-perturbative partition function including contributions from all the real instantons, which is real for positive modulus and string coupling. We also explore complex instantons and find two infinite towers of them. We expect them to correspond to BPS states in type II string.

China

Jiashen Chen

Jie Gu

Xin Wang

Resurgent structure of 2d Yang-Mills theory on a torus

We study $$ \mathcal{N} $$ = 4 super Yang-Mills theory compactified on an S at zero temperature, with VEVs for two scalar bilinears and three independent current sources. We show that type IIB supergravity provides a complete holographic description of this setup, admitting both supersymmetric and non-supersymmetric AdS-soliton solutions that are asymptotically AdS and smooth in the IR. The current sources correspond in 2+1 dimensions to Q-ball charge densities for U(1) ⊂ SO(6) , and are geometrically realized as twists along three angular directions of the S . We demonstrate that the bulk dynamics encodes the full vacuum structure of the dual field theory and explicitly reconstruct the supersymmetric moduli space.

Brazil

Chile

Andrés Anabalón

Horatiu Nastase

United Kingdom

Carlos Nunez

Spain

Marcelo Oyarzo

Ricardo Stuardo

Moduli space of $$ \mathcal{N} $$ = 4 super Yang-Mills from AdS/CFT

We study three Type II supergravity solutions holographically dual to codimension-2 supersymmetric defects in ($\textit{p}$ + 1)-dimensional SU($\textit{N}$) maximally supersymmetric Yang-Mills theory ($\textit{p}$ = 2, 3, 4). In all of these cases, the defects have a non-trivial monodromy for the maximal abelian subgroup of the SO(9 – $\textit{p}$) R-symmetry. Such solutions are obtained by considering branes wrapping spindle configurations, changing the parameters (which alters the coordinate domain), and imposing suitable boundary conditions. We provide a prescription to compute the entanglement entropy of the effective theory on the defect. We find the resulting quantity to be proportional to the free energy of the ambient theory. A similar analysis is performed for the D5-brane wrapping a spindle, but we find that changing the coordinate domain does not lead to a defect solution, but rather to a circle compactification.

Andrea Conti

Monodromy defects in maximally supersymmetric Yang-Mills theories from holography

We consider planar $$ \mathcal{N} $$ = 4 super Yang-Mills at finite temperature with chemical potentials that couple either to the $\textit{R}$-charges or the spins of the operators. We find expressions for the Hagedorn temperatures at both zero coupling by explicitly counting states, and at strong coupling using the string theory dual. We then apply the quantum spectral curve (QSC) to this problem, which adds additional twists to the $\textit{Q}$-functions. For a single chemical potential $\textit{μ}$ coupled to one of the $\textit{R}$-charges, we find the analytic weak-coupling Hagedorn temperature to one-loop order for any value of $\textit{μ}$, and to two-loop order for $\textit{μ}$ = 1/2. We then solve the QSC numerically, showing that at strong coupling there is good agreement with the string theory prediction to order 1/$\textit{λ}$ . This provides further evidence for a recent conjecture of Harmark for the form of the world-sheet zero-point shift. We also use the QSC to find the analytic one-loop correction to the Hagedorn temperature with non-zero chemical potentials coupled to the spins.

Sweden

Simon Ekhammar

United States

Joseph Minahan

Charles Thull

Twisting the Hagedorn temperature in planar $$ \mathcal{N} $$ = 4 super Yang-Mills

In this paper, we construct an explicit rephasing transformation that converts an arbitrary unitary mixing matrix into the Fritzsch–Xing (FX) parametrization, which is obtained by trivializing arguments of the matrix elements in the third row and third column. We further analyze rephasing invariant structure of the FX phase <italic>&#948;</italic> <inf>FX</inf> under an approximation <math altimg='si1.svg'><mrow><msubsup><mi>U</mi><mrow><mn>13</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, where the 1&#8211;3 element of the diagonalization matrix of charged leptons <italic>Ue</italic> is neglected. With an additional approximation <math altimg='si2.svg'><mrow><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup><mo linebreak='goodbreak'>=</mo><mn>0</mn></mrow></math>, the FX phase becomes highly simplified, reducing to a sum of the neutrino-intrinsic FX phase <math altimg='si3.svg'><msubsup><mi>&#948;</mi><mrow><mrow><mi mathvariant='normal'>F</mi></mrow><mi>X</mi></mrow><mi>&#957;</mi></msubsup></math> and the contribution from the relative phase <math altimg='si4.svg'><mrow><msubsup><mi>&#961;</mi><mn>1</mn><mo>&#8242;</mo></msubsup><mo linebreak='goodbreak'>&#8722;</mo><msubsup><mi>&#961;</mi><mn>2</mn><mo>&#8242;</mo></msubsup></mrow></math> between the lighter 1-2 generations. The phase <italic>&#948;</italic> <inf>FX</inf> for finite <math altimg='si5.svg'><msubsup><mi>U</mi><mrow><mn>23</mn></mrow><mi>e</mi></msubsup></math> is understood as a generalization of the compact expression. This result covers almost all perturbative calculations of CP phases for the CKM and MNS matrices with hierarchical charged fermions.

Masaki J.S. Yang

Rephasing invariant structure of CP phase in Fritzsch–Xing parametrization for simplified mixing matrices

We consider planar codimension-one defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills (SYM) theory, realized by the D3/D5-brane intersection. Working in the probe limit, where the number of D5-branes is small compared to the number of D3-branes, we obtain analytic results for the holographic entanglement entropy of a ball-shaped region centered on the defect. A defect renormalization group flow is triggered by giving the defect hypermultiplets a mass, which corresponds to separating the D3- and D5-branes. Along this flow the entanglement C-function decreases monotonically. We also allow the D5-branes to carry worldvolume flux corresponding to dissolved D3-branes, in which case the setup describes an interface between two copies of $$ \mathcal{N} $$ = 4 SYM theory with different gauge groups, where an RG flow is triggered by placing one side of the interface onto the Coulomb branch. Here we again find monotonic behavior of the entanglement C-function, although its interpretation as a measure of effective degrees of freedom is problematic. We investigate possible alternative measures of degrees of freedom.

Finland

Niko Jokela

Germany

Jani Kastikainen

José Penín

Ronnie Rodgers

Helime Ruotsalainen

Entanglement C-functions of defects and interfaces in $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills theory

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>16</mn><mn>3</mn></msup><mo>×</mo><mn>8</mn></math> lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero and the fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-Weiss periodicity, which are exact properties of the quantum chromodynamics free energy. We use this ansatz to estimate the position of Lee-Yang zeros in the complex chemical potential plane. The temperature dependence of the imaginary part of the Lee-Yang zeros is then fitted with ansätze motivated by the universal behavior of the free energy near a 3D Ising critical point. In principle, this allows one to estimate the temperature of the critical endpoint. We consider several sources of systematic errors. On this single lattice spacing, we find that with 84% probability the chiral critical endpoint is either below 103 MeV temperature or it does not exist. We also identify some caveats of the method, which do not disappear even with the extremely high statistics of this present study. We discuss to what extent these can be eliminated by future high statistics lattice analyses.

Alexander Adam

Szabolcs Borsányi

Hungary

Zoltán Fodor

Jana N. Guenther

Piyush Kumar

Paolo Parotto

Attila Pásztor

Chik Him Wong

High-precision baryon number cumulants from lattice QCD in a finite box: Cumulant ratios, Lee-Yang zeros, and critical endpoint predictions

A first-order, confinement/deconfinement phase transition appears in the finite temperature behavior of many non-Abelian gauge theories. These theories play an important role in proposals for completion of the Standard Model of particle physics, hence the phase transition might have occurred in the early stages of evolution of our Universe, leaving behind a detectable relic stochastic background of gravitational waves. Lattice field theory studies implementing the density of states method have the potential to provide detailed information about the phase transition, and measure the parameters determining the gravitational-wave power spectrum, by overcoming some of the challenges faced by importance-sampling methods. We assess this potential for a representative choice of Yang-Mills theory with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>S</mi><mi>p</mi><mo stretchy="false">(</mo><mn>4</mn><mo stretchy="false">)</mo></math> gauge group. We characterize its finite-temperature, first-order phase transition, in the thermodynamic (infinite volume) limit, for two different choices of number of sites in the compact time direction, hence taking the first steps toward the continuum limit extrapolation. We demonstrate the persistence of nonperturbative phenomena associated to the first-order phase transition: coexistence of states, metastability, latent heat, surface tension. We find consistency between several different strategies for the extraction of the volume-dependent critical coupling, hence assessing the size of systematic effects. We also determine the minimum choice of ratio between spatial and time extent of the lattice that allows one to identify the contribution of the surface tension to the free energy. We observe that this ratio scales nontrivially with the time extent of the lattice, and comment on the implications for future high-precision numerical studies.

Ed Bennett

Biagio Lucini

David Mason

Maurizio Piai

Enrico Rinaldi

Davide Vadacchino

Fabian Zierler

Finite-temperature Yang-Mills theories with the density of states method: Toward the continuum limit