We construct defect networks in pure Yang-Mills theory in two dimensions using a refinement of the lattice approach. The refinement preserves the locality properties of individual defects, and is compatible with solvability of the theory via subdivision invariance. We explicitly demonstrate closure of the building blocks under fusion.

Italy

Luca Griguolo

United Kingdom

Elisa Marieni

Itamar Yaakov

Lattice defect networks in 2d Yang-Mills

We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that surface. Firstly, we argue that the algebraic structure that underlies the large $\textit{N}$ limit of the chiral gauge theory is a partial permutation algebra of observables which codes covering maps of all degrees simultaneously. Secondly, we exploit the Gromov-Witten/Hurwitz correspondence to interpret chiral Yang-Mills theory as a finite deformation of a Gromov-Witten theory by an area-dependent transposition interaction and an operator that codes a compactification of Hurwitz space. The proposed string dual manifestly includes an integral over the moduli space of Riemann surfaces as well as the identification of closed string states as completed cycles.

France

Lior Benizri

Jan Troost

The string dual to two-dimensional Yang-Mills theory

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, <math altimg='si1.svg'><mi>s</mi><mo stretchy='false'>(</mo><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><mo stretchy='false'>)</mo><mo stretchy='false'>/</mo><msubsup><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow><mrow><mn>3</mn></mrow></msubsup></math>, on both sides of the transition and determine the latent heat <italic>h</italic>. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate <math altimg='si2.svg'><mi>h</mi><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>1.175</mn><mo stretchy='false'>(</mo><mn>10</mn><mo stretchy='false'>)</mo></math>. Additionally, we determine the critical temperature <math altimg='si3.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math> in physical units with permille accuracy, yielding <math altimg='si4.svg'><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub><msqrt><mrow><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msqrt><mo linebreak='goodbreak' linebreakstyle='after'>=</mo><mn>0.24915</mn><mo stretchy='false'>(</mo><mn>29</mn><mo stretchy='false'>)</mo></math>. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for <italic>T</italic> between 0 and <math altimg='si5.svg'><mn>3.4</mn><msub><mrow><mi>T</mi></mrow><mrow><mi>c</mi></mrow></msub></math>.

Leonardo Giusti

Mitsuaki Hirasawa

Michele Pepe

Luca Virzì

A precise study of the thermodynamic properties of the SU(3) Yang-Mills theory across the deconfinement transition

We use a loop truncated Jevicki-Sakita effective collective field Hamiltonian to obtain, over a very large range of values of 't Hooft's coupling, and directly in the large <italic>N</italic> limit, the large <italic>N</italic> (planar) ground state energy, the planar ground state expectation values of invariant correlators, and the <math altimg='si1.svg'><mn>1</mn><mo stretchy='false'>/</mo><mi>N</mi></math> spectrum of the quantum mechanical system of three massless Yang-Mills coupled matrices. This captures the dynamics of the (residual) gauge invariant sector of the spatially reduced <math altimg='si2.svg'><mn>3</mn><mo linebreak='goodbreak' linebreakstyle='after'>+</mo><mn>1</mn></math> dimensional pure Yang-Mills theory, in the large <italic>N</italic> limit. The large <italic>N</italic> loop space constraints are handled by the use of master variables. As is the case for two matrices, the method is highly efficient directly in the massless limit, and it reproduces to a very high precision the scaling dependence of physical quantities, determined by their dimensions, on the dimensionful 't Hooft coupling. We obtain the bound state masses of &#8220;glueballs&#8221;, their quantum numbers and ensuing degeneracies.

South Africa

João P. Rodrigues

“Glueballs” in the quantum mechanics of three large massless Yang-Mills coupled matrices

We holographically study the far-from-equilibrium isotropization dynamics of the strongly coupled $$ \mathcal{N} $$ = 4 supersymmetric Yang-Mills plasma. The dual gravitational background is driven to be out of equilibrium and anisotropic by a time-dependent change in boundary conditions. At late times, the system relaxes and asymptotically approaches a static configuration. The large initial energy densities accelerate the isotropization significantly compared to the initial geometry corresponding to the supersymmetric Yang-Mills vacuum. We analyze shear transport during isotropization by directly computing the time-dependent stress tensor, which is now a nonlinear function of the shear rate. The shear viscosity far from equilibrium displays much richer dynamics than its near-equilibrium counterpart. Moreover, we uncover that the equilibrium viscosity-to-entropy ratio at late times depends on the details of the quench function and the initial data, which could be due to a resummation of the hydrodynamic description. In particular, this ratio can be parametrically smaller than the Kovtun-Son-Starinets bound calculated from linear response theory.

China

Shoucheng Wang

Germany

Song He

Li Li

Shear transport in far-from-equilibrium isotropization of supersymmetric Yang-Mills plasma

In this work, we compute the two-loop result of the null hexagonal Wilson loop with a Lagrangian insertion in planar, maximally supersymmetric Yang-Mills theory via a bootstrap approach. Normalized by the null polygonal Wilson loop itself, the integrand-level result of this observable corresponds to the logarithm of the six-point three-loop amplitude in this theory, while its integrated result is conjectured to match the maximally transcendental part of the six-point three-loop all-plus amplitude in pure Yang-Mills theory. Our work builds on two recent advances. On the one hand, the set of leading singularities relevant to this observable was recently classified. On the other hand, the relevant space of special functions that may in principle accompany these leading singularities was determined at two loops and for six particles by a dedicated Feynman integral calculation. These two ingredients serve as the foundation of our bootstrap ansatz. We fix all indeterminates in this ansatz by imposing physical constraints, such as symmetries, absence of spurious divergences, and correct behavior in soft and collinear limits. Finally, we discuss and verify certain physical properties of our symbol result, including physical singularities, behavior under multi-Regge limit, as well as Steinmann relations between symbol entries. The latter relations are motivated by the correspondence to all-plus amplitudes in pure Yang-Mills theory, and successfully checking them constitutes a consistency check of this conjectured correspondence.

Sérgio Carrôlo

Dmitry Chicherin

Johannes Henn

Qinglin Yang

Yang Zhang

Hexagonal Wilson loop with Lagrangian insertion at two loops in $$ \mathcal{N} $$ = 4 super Yang-Mills theory

<p>The structure of center vortices is studied in SU(4) Yang-Mills theory for the first time to illuminate the interplay between elementary (center charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>±</mo><mn>1</mn></math>) and doubly charged vortices. Unlike in SU(3), where charge <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>+</mo><mn>2</mn></math> vortices are simply elementary vortices with reversed orientations in spacetime, these possibilities are physically distinct in SU(4). Visualizations of the vortex structure in three-dimensional slices reveal the various ways in which doubly charged objects manifest, as the convergence and matching of elementary vortices or as isolated doubly charged loops. An algorithm is described to classify every doubly charged chain as one of these three types. A collection of vortex statistics is considered to quantify the vortex structure. Many of these pertain to the novel doubly charged objects, including their relative proportions and chain lengths, which are analyzed to highlight the differences between each chain type. Three different lattice spacings are employed to investigate the approach to the continuum limit. Vortex matching chains are found to be shorter on average but also more prevalent than vortex convergences, ascribed to their interpretation as extended center monopoles. In addition, the lengths of both vortex convergences and vortex matchings are observed to follow an exponential distribution, allowing the introduction of a constant probability for a doubly charged chain to split into two elementary vortices as it propagates. Combined, these findings provide a characterization of the vortices that comprise center-vortex structures in SU(4) Yang-Mills theory.</p>

Australia

Jackson A. Mickley

Derek B. Leinweber

Brazil

Luis E. Oxman

Structure of center-vortex matter in SU(4) Yang-Mills theory

<p>Without invoking any cumulant determination at the input level, we present here the first calculations of direct estimates of the Lee-Yang zeros of the QCD partition function in (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math>)-flavor QCD. These zeros are obtained in the complex isospin chemical potential <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>I</mi></msub></math> plane using the unbiased exponential resummation formalism on <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>N</mi><mi>τ</mi></msub><mo>=</mo><mn>8</mn></math> lattices and with physical quark masses. For different temperatures, we illustrate the stability of the zeros closest to the origin from which we subsequently procure the radius of convergence estimates. From the temperature-dependence study of the real and imaginary parts of these zeros, we try estimating one of the possible critical points forming the second-order pion condensate critical line in the isospin phase diagram. Further, we compare these resummed estimates with the corresponding Mercer-Roberts estimates of the subsequent Taylor series expansions of the first three partition function cumulants. We also outline comparisons between resummed and Taylor series results of these cumulants for real and imaginary values of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>I</mi></msub></math> and highlight the behavior of different expansion orders within and beyond the obtained resummed estimates of the radius of convergence. We also reestablish that this resummed radius of convergence can efficiently capture the onset of the overlap problem for finite real <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><mi>I</mi></msub></math> simulations.</p>

Sabarnya Mitra

Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice

For the spinning superparticle we construct the pull-back of the world-line path integral to super moduli space in the Hamiltonian formulation. We describe the underlying geometric decomposition of super moduli space. Algebraically, this gives a realization of the cyclic complex. The resulting space-time action is classically equivalent to Yang-Mills theory up to boundary terms and additional non-local interactions.

Carlo Cremonini

Ivo Sachs

Yang-Mills theory from super moduli space

We consider four-point functions of protected, double- and single-trace operators in the large central charge limit. We use superconformal symmetry to disentangle the contribution of protected operators in the partial wave decomposition. With this information, we fix the non-protected part of such correlators up to subleading order in the large central charge expansion. We particularly focus on the triple-trace sector of the correlator and comment on the connection to the holographic description of these correlators.

Sweden

Agnese Bissi

United States

Giulia Fardelli

Andrea Manenti

Composite operators in $$ \mathcal{N} $$ = 4 Super Yang-Mills