Related papers: On the May Spectral Sequence at the prime 2

The Mayer cluster expansion technique is applied to the Nekrasov instanton partition function of $\mathcal{N}=2$ $SU(N_c)$ super Yang-Mills. The subleading small $\epsilon_2$-correction to the Nekrasov-Shatashvili limiting value of the…

We use $K_4^-$ to denote the graph obtained from $K_4$ by removing an edge, and use $TK_5$ to denote a subdivision of $K_5$. Let $G$ be a 5-connected nonplanar graph and $\{x_1,x_2,y_1,y_2\}\subseteq V(G)$ such that $G[\{x_1,x_2,$…

In this work we establish several monotonicity and decomposition results in the framework of random regular graphs. Among other results, we show that, for a wide range of parameters $d_1 \leq d_2$, there exists a coupling of $G(n,d_1)$ and…

Motivated by questions of present interest in nuclear and condensed matter physics we consider the superposition of a diagonal matrix with independent random entries and a GUE. The relative strength of the two contributions is determined by…

We propose an extension of the su(2,2|4) superalgebra to incorporate the $F1/D1$ string charges in type IIB string theory on the $AdS_{5} \times S^{5}$ background, or the electro-magnetic charges in the dual super Yang-Mills theory. With…

We consider Yang-Mills theory with N=2 super translation group in ten auxiliary dimensions as the structure group. The gauge theory is defined on a direct product manifold \Sigma_2\times H^2, where \Sigma_2 is a two-dimensional Lorentzian…

A non-perturbative confinement mechanism has been proposed to explain the fate of the unbroken gauge group on the world-volume of annihilating D-brane-anti-D-brane pairs. In this paper, we examine this phenomenon closely from several…

We introduce gauge theories based on a class of disconnected gauge groups, called principal extensions. Although in this work we focus on 4d theories with N=2 SUSY, such construction is independent of spacetime dimensions and supersymmetry.…

In this paper we investigate the class of invariant positive definite kernels on the free semigroup on N generators. We provide a combinatorial description of the positivity of the kernel in terms of Dyck paths and then we find a…

We give a master formula for the spin-2 spectrum of a class of three-dimensional Chern-Simons theories at large $N$, with flavour group containing SU(3), that arise as infrared fixed points of the D2-brane worldvolume field theory and have…

A. Reid showed that if $\Gamma_1$ and $\Gamma_2$ are arithmetic lattices in $G = \operatorname{PGL}_2(\mathbb R)$ or in $\operatorname{PGL}_2(\mathbb C)$ which give rise to isospectral manifolds, then $\Gamma_1$ and $\Gamma_2$ are…

This paper is an extended version of our previous short letter \cite{ZG2} and is attempted to give a detailed account for the results presented in that paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra and…

We construct the low-energy effective field theory for a D3-brane in constant R-R 2-form potential background as the S-dual theory of a D3-brane in NS-NS B-field background. Despite the non-Abelian algebra of the noncommutative U(1) gauge…

We develop a general theory of $W$-algebras in the context of supersymmetric vertex algebras. We describe the structure of $W$-algebras associated with odd nilpotent elements of Lie superalgebras in terms of their free generating sets. As…

In this paper, we present a method to obtain regular (or equitable) partitions of Cayley (di)graphs (that is, graphs, digraphs, or mixed graphs) of permutation groups on $n$ letters. We prove that every partition of the number $n$ gives…

We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexes: the $0$-degree \"uberhomology. Consequently, we obtain a…

We construct a spectral sequence for L2-type cohomology groups of discrete measured groupoids. Based on the spectral sequence, we prove the Hopf-Singer conjecture for aspherical manifolds with poly-surface fundamental groups. More…

Duality is an indispensable tool for describing the strong-coupling dynamics of gauge theories. However, its actual realization is often quite subtle: quantities such as the partition function can transform covariantly, with degrees of…

There is an established bijection between finite-index subgroups Gamma of Gamma(2) and bipartite graphs on surfaces, or, equivalently, certain triples of permutations. We utilize this relationship to study both congruence and noncongruence…

Thin growing tissues (such as plant leaves) can be modelled by a bounded domain $S\subset R^2$ endowed with a Riemannian metric $g$, which models the internal strains caused by the differential growth of the tissue. The elastic energy is…