Fri·Sep 3, 2021Friday·September 3, 2021

1. 01*

   Exact duality and local dynamics in SU(N) lattice gauge theory

   Manu Mathur🇮🇳 · Atul Rathor🇮🇳

   We construct exact duality transformations in pure SU(N) Hamiltonian lattice gauge theory in (2+1) dimension. This duality is obtained by making a series of iterative canonical transformations on the SU(N) electric vector fields and their conjugate magnetic vector potentials on the four links around every plaquette. The resulting dual description is in terms of the magnetic scalar fields or plaquette flux loops and their conjugate electric scalar potentials. Under SU(N) gauge transformations they both transform like adjoint matter fields. The dual Hamiltonian describes the nonlocal self-interactions of these plaquette flux loops in terms of the electric scalar potentials and with inverted coupling. We show that these nonlocal loop interactions can be made local and converted into minimal couplings by introducing SU(N) auxiliary gauge fields along with new plaquette constraints. The matter fields can be included through minimal coupling. The techniques can be easily generalized to (3+1) dimensions.

   hep-latPRD(2023)·9 citations
2. 02*

   Large-$N$ limit of two-dimensional Yang--Mills theory with four supercharges

   Navdeep Singh Dhindsa🇮🇳 · Raghav G. Jha🇨🇦 · Anosh Joseph🇮🇳 · David Schaich🇬🇧

   We study the two-dimensional Yang--Mills theory with four supercharges in the large-$N$ limit. By using thermal boundary conditions, we analyze the internal energy and the distribution of scalars. We compare their behavior to the maximally supersymmetric case with sixteen supercharges, which is known to admit a holographic interpretation. Our lattice results for the scalar distribution show no visible dependence on $N$ and the energy at strong coupling appears independent of temperature.

   hep-lathep-thPoS(2022)·6 citations
3. 03*

   Tracy-Widom method for Janossy density and joint distribution of extremal eigenvalues of random matrices

   Shinsuke M. Nishigaki🇯🇵

   The Jánossy density for a determinantal point process is the probability density that an interval $I$ contains exactly $p$ points except for those at $k$ designated loci. The Jánossy density associated with an integrable kernel $\mathbf{K}\doteq (\phi (x)\psi (y)-\psi (x)\phi (y))/(x-y)$ is shown to be expressed as a Fredholm determinant $\mathrm{Det}(\mathbb{I}-\tilde{\mathbf{K}}{|}_I)$ of a transformed kernel $\tilde{\mathbf{K}}\doteq (\tilde{\phi }(x)\tilde{\psi }(y)-\tilde{\psi }(x)\tilde{\phi }(y))/(x-y)$. We observe that $\tilde{\mathbf{K}}$ satisfies Tracy and Widom's criteria if $\mathbf{K}$ does, because of the structure that the map $(\phi ,\psi )\mapsto (\tilde{\phi },\tilde{\psi })$ is a meromorphic $\mathrm{SL}(2,\mathbb{R})$ gauge transformation between covariantly constant sections. This observation enables application of the Tracy--Widom method to Jánossy densities, expressed in terms of a solution to a system of differential equations in the endpoints of the interval. Our approach does not explicitly refer to isomonodromic systems associated with Painlevé equations employed in the preceding works. As illustrative examples we compute Jánossy densities with $k=1,p=0$ for Airy and Bessel kernels, related to the joint distributions of the two largest eigenvalues of random Hermitian matrices and of the two smallest singular values of random complex matrices.

   ↳ math-phcond-mat.dis-nnhep-lathep-th+2PTEP(2021)·2 citations
4. 04*

   Higher Dimensional Polytopal Universe in Regge Calculus

   Ren Tsuda🇯🇵 · Takanori Fujiwara🇯🇵

   Higher dimensional closed Friedmann-Lemaître-Robertson-Walker (FLRW) universe with positive cosmological constant is investigated by Regge calculus. A Cauchy surface of discretized FLRW universe is replaced by a regular polytope in accordance with the Collins-Williams (CW) formalism. Polytopes in an arbitrary dimensions can be systematically dealt with by a set of five integers integrating the Schläfli symbol of the polytope. Regge action in continuum time limit is given. It possesses reparameterization invariance of the time variable. Variational principle for edge lengths and struts yields Hamiltonian constraint and evolution equation. They describe oscillating universe in dimensions larger than three. To go beyond the approximation by regular polytopes, we propose pseudo-regular polytopes with fractional Schläfli symbols as a substitute for geodesic domes in higher dimensions. We examine the pseudo-regular polytope model as an effective theory of Regge calculus for the geodesic domes. In the infinite frequency limit, the pseudo-regular polytope model reduces to the continuum FLRW universe.

   ↳ gr-qchep-lathep-thPTEP(2022)·0 citations

* Reconstructed cohort: no mailing for this day survives in the archive. Papers are grouped by their submission times and arXiv's announcement cut-off, assuming announcement without delay; positions follow identifier order. Validated at ~91% exact-day agreement against the archived era.