In many gauge theories at different values of parameters entering Lagrangian, the vacuum is dominated by coherent condensates of different mutually non-local fields (for instance, by condensates of electric or magnetic charges, or by various dyons). It is argued that the transition between these ”dual to each other” phases proceeds through an intermediate ”mixed phase”, having qualitatively dif...

We discuss non-compact SL(2, R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.

We study a problem of low-energy effective action in N=4 super Yang-Mills theories. Using harmonic superspace approach we consider N=4 SYM in terms of unconstrained N=2 superfield and apply N=2 background field method to finding effective action for N=4 SU(n) SYM broken down to U(n)n−1. General structure of leading low-energy corrections to effective action is discussed and calculational proced...

Non-perturbative predictions and numerical simulations in supersymmetric Yang-Mills (SYM) theories are reviewed.

Jung et al. [7] introduced a geometric structure on Sym+(p), the set of p×p symmetric positive-definite matrices, based eigen-decomposition. Eigenstructure determines both stratification defined by eigenvalue multiplicities, and fibers “eigen-composition” map F:M(p):=SO(p)×Diag+(p)→Sym+(p). When M(p) is equipped with suitable Riemannian metric, fiber leads to notions scaling-rotation distance b...

Given two positive integers n?3 and t?n, the permutations ?,??Sym(n) are t-setwise intersecting if they agree (setwise) on a t-subset of {1,2,…,n}. A family F?Sym(n) is any F intersecting. Ellis (2012) [6] conjectured that t?n family, then |F|?t!(n?t)! equality holds only coset setwise stabilizer In this paper, we prove n?11 3-setwise intersecting, |F|?6(n?3)!. Moreover, characteristic vector m...

For Ω an infinite set, k ≥ 2 and W the set of k-sets from Ω, there is a natural closed permutation group Γk which is a non-split extension 0 → Z 2 → Γk → Sym(Ω) → 1. We classify the closed subgroups of Γk which project onto Sym(Ω). The question arises in model theory as a problem about finite covers, but here we formulate and solve it in algebraic terms.

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.

We interpret quasi-symmetric functions and noncommutative symmetric functions as characters of a degenerate quantum group obtained by putting q = 0 in a variant of U q (gl N). R esum e: Nous interpr etons les fonctions quasi-sym etriques et les fonctions sym etriques non commu-tatives comme caract eres d'un groupe quantique d eg en er e obtenu en posant q = 0 dans une variante de U q (gl N).

We consider the radial quantization of N = 4 super Yang-Mills (SYM) in 4 dimensions, i.e., N = 4 SYM on a cylinder R × S 3. We construct the generators of superconformal symmetry in the case of U (N) gauge group, generalizing the earlier work by Nicolai et al. for U (1) gauge group. We study how these generators contract to the symmetry of pp-wave when they act on a state with large R-charge.