Related papers: New sum rule identities and duality relation for t…
We calculate transition probabilities for various processes involving giant gravitons and small gravitons in AdS space, using the dual N=4 SYM theory. The normalization factors for these probabilities involve, in general, correlators for…
In this paper we investigate the distribution of the set of values of a quadratic form Q, at integral points. In particular we are interested in the n-point correlations of the this set. The asymptotic behaviour of the counting function…
We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which…
We investigate the operator content of the Q-state Potts model in arbitrary dimension, using the representation theory of the symmetric group. In particular we construct all possible tensors acting on N spins, corresponding to given…
We extend a recent analysis of the $q$-states Potts model on an ensemble of random planar graphs with $p\leqslant q$ allowed, equally weighted, spins on a connected boundary. In this paper we explore the $(q<4,p\leqslant q)$ parameter space…
We summarise the status of an intriguing new duality between planar maximally helicity violating scattering amplitudes and light-like Wilson loops in N=4 super Yang-Mills. In particular, we focus on the role played by (dual) conformal…
The Kramers-Wannier duality is shown to hold for all the even number spin correlation functions of the two dimensional square lattice Ising model in the sense that the high temperature $(T>T_{c})$ expressions for these correlation functions…
A sequence $(x_n)_{n=1}^{\infty}$ on the torus $\mathbb{T} \cong [0,1]$ is said to exhibit Poissonian pair correlation if the local gaps behave like the gaps of a Poisson random variable, i.e. $$ \lim_{N \rightarrow \infty}{ \frac{1}{N} \#…
We give bijective results between several variants of lattice paths of length $2n$ (or $2n-2$) and integer compositions of n, all enumerated by the seemingly innocuous formula $4^{n-1}$. These associations lead us to make new connections…
We study long-range correlation functions of the rectangular Ising lattice with cyclic boundary conditions. Specifically, we consider the situation in which two spins are on the same column, and at least one spin is on or near free…
We consider the O(n) theory in the $n \to 0$ limit. We show that the theory is described by logarithmic conformal field theory, and that the correlation functions have logarithmic singularities. The explicit forms of the two-, three- and…
We study four-point correlators in superconformal theories in various dimensions. We develop an efficient method to solve the superconformal Ward identities in Mellin space. For 4d $\mathcal{N}=4$ SYM and the 6d $\mathcal{N}=(2,0)$ theory,…
We investigate duality properties of N-form fields, provide a symmetric way of coupling them to electric/magnetic sources, and check that these charges obey the appropriate quantization requirements. First, we contrast the D=4k case, in…
For general N=5 and N=6 superconformal field theories in three dimensions, we compute the three-point correlation functions of the supercurrent multiplets. In each case, N=5 and N=6, the functional form of this correlator is uniquely fixed…
We revisit in this paper the problem of connectivity correlations in the Fortuin-Kasteleyn cluster representation of the two-dimensional $Q$-state Potts model conformal field theory. In a recent work [M. Picco, S. Ribault and R.…
The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution…
We consider q-state Potts models coupled by their energy operators. Restricting our study to self-dual couplings, numerical simulations demonstrate the existence of non-trivial fixed points for 2 <= q <= 4. These fixed points were first…
Among the knots that are the connected sum of two torus knots with cobordism distance 1, we characterize those that have 4-dimensional clasp number at least 2, and we show that their n-fold connected self-sum has 4-dimensional clasp number…
We consider 1+1 D theories which are free everywhere except for cosine and magnetic interactions on the boundary. These theories arise in dissipative quantum systems, open string theory, and, in special cases, tunneling in quantum Hall…
This paper proves a "new" family of functional equations (Eqn) for Rogers dilogarithm. These equations rely on the combinatorics of dihedral coordinates on moduli spaces of curves of genus 0, M 0,n. For n = 4 we find back the duality…