Related papers: Ward Identities for the 2PI effective action in QE…
Second-order variational properties have been shown to play important theoretical and numerical roles for different classes of optimization problems. Among such properties, twice epi-differentiability has a special place because of its…
The superconformal Ward identities combined with N=2 harmonic analyticity are used to evaluate two-loop four-point correlation functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory in terms of the well-known…
We find necessary and sufficient conditions for gauge invariance of the action of Double Field Theory (DFT) as well as closure of the algebra of gauge symmetries. The so-called weak and strong constraints are sufficient to satisfy them, but…
In this paper we derive a hierarchy of integral equations from the 4PI effective action which have the form of Bethe-Salpeter equations. We show that the vertex functions defined by these equations can be used to truncate the exact…
We prove several results about integral versions of Fourier duality for abelian schemes, making use of Pappas's work on integral Grothendieck-Riemann-Roch. If $S$ is smooth quasi-projective of dimension $d$ over a field and $\pi \colon X\to…
Recently, the leading soft gluon theorem with single soft emission was shown to be the Ward identity of a two dimensional $\cal G$-Kac-Moody symmetry. In this note, we show that the leading soft gluon theorem can be interpreted as the Ward…
In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…
The exact prepotential for $N = 2$ supersymmetric Yang-Mills theory is derived from the superconformal anomalous Ward identity for the gauge group SU(2) and SU(3) which can be generalized to any other rank two gauge group.
We study systematically the higher order corrections to the parity violating part of the effective action for the Abelian Chern-Simons theory in 2+1 dimensions, using the method of derivative expansion. We explicitly calculate the parity…
This paper proposes some efficient and accurate adaptive two-grid (ATG) finite element algorithms for linear and nonlinear partial differential equations (PDEs). The main idea of these algorithms is to utilize the solutions on the $k$-th…
In this paper, our focus lies on the study of the second-order variational analysis of orthogonally invariant matrix functions. It is well-known that an orthogonally invariant matrix function is an extended-real-value function defined on…
Four-point correlation functions of hypermultiplet bilinear composites are analysed in N=2 superconformal field theory using the superconformal Ward identities and the analyticity properties of the composite operator superfields. It is…
We study the gauge dependence of the one-loop effective action for the abelian $6D$, ${\cal N}=(1,0)$ supersymmetric gauge theory formulated in harmonic superspace. We introduce the superfield $\xi$-gauge, construct the corresponding gauge…
We consider the two-point function of the totally asymmetric simple exclusion process with stationary initial conditions. The two-point function can be expressed as the discrete Laplacian of the variance of the associated height function.…
We discuss the following aspects of two-dimensional N=2 supersymmetric theories defined on compact super Riemann surfaces: parametrization of (2,0) and (2,2) superconformal structures in terms of Beltrami coefficients and formulation of…
We derive an alternative to the Wetterich-Morris-Ellwanger equation by means of the two-particle irreducible (2PI) effective action, exploiting the method of external sources due to Garbrecht and Millington. The latter allows the two-point…
A minimal truncated set of the integral Dyson-Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations…
We use Ward identities derived from the generalized Konishi anomaly in order to compute effective superpotentials for SU(N), SO(N) and $Sp(N)$ supersymmetric gauge theories coupled to matter in various representations. In particular we…
We present an analytical and numerical study of scalar phi^4 theory at finite temperature with a renormalized 2-loop truncation of the 2PI effective action.
Based on bulk reconstruction from the finite boundary of the Bruhat-Tits tree, the boundary effective theory is obtained after integrating out fields outside this boundary. According to the $~p$-adic version of Anti-de Sitter/Conformal…