Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userPolyakov relation for the sphere and higher genus surfaces
106
0
0.0
(
0
)
Authors
Pietro Menotti
Ask ChatGPT about the research
No Arabic abstract
The Polyakov relation, which in the sphere topology gives the changes of the Liouville action under the variation of the position of the sources, in the case of higher genus is related also to the dependence of the action on the moduli of the surface. We write and prove such a relation for genus 1 and for all hyperelliptic surfaces.
rate research
Read More
We study the Polyakov line in Yang-Mills matrix models, which include the IKKT model of IIB string theory. For the gauge group SU(2) we give the exact formulae in the form of integral representations which are convenient for finding the asymptotic behaviour. For the SU(N) bosonic models we prove upper bounds which decay as a power law at large momentum p. We argue that these capture the full asymptotic behaviour. We also indicate how to extend the results to some correlation functions of Polyakov lines.
We give an explicit superspace construction of higher spin conserved supercurrents built out of $4D,mathcal{N}=1$ massless supermultiplets of arbitrary spin. These supercurrents are gauge invariant and generate a large class of cubic interactions between a massless supermultiplet with superspin $Y_1=s_1+1/2$ and two massless supermultiplets of arbitrary superspin $Y_2$. These interactions are possible only for $s_1geq 2Y_2$. At the equality, the supercurrent acquires its simplest form and defines the supersymmetric, higher spin extension of the linearized Bel-Robinson tensor.
We describe an iterative scheme which allows us to calculate any multi-loop correlator for the complex matrix model to any genus using only the first in the chain of loop equations. The method works for a completely general potential and the results contain no explicit reference to the couplings. The genus $g$ contribution to the $m$--loop correlator depends on a finite number of parameters, namely at most $4g-2+m$. We find the generating functional explicitly up to genus three. We show as well that the model is equivalent to an external field problem for the complex matrix model with a logarithmic potential.
Lorentz invariance is broken for the non-Abelian monopoles. Here we will consider the case of t Hooft-Polyakov monopole and show that the Lorentz invariance of its field will be restored using Dirac quantization.
The Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and Backlund transformations of certain type. We study the Wahlquist-Estabrook algebra of the n-dimensional generalization of the Landau-Lifshitz equation and construct an epimorphism from this algebra onto an infinite-dimensional quasigraded Lie algebra L(n) of certain matrix-valued functions on an algebraic curve of genus 1+(n-3)2^{n-2}. For n=3,4,5 we prove that the Wahlquist-Estabrook algebra is isomorphic to the direct sum of L(n) and a 2-dimensional abelian Lie algebra. Using these results, for any n a new family of Miura type transformations (differential substitutions) parametrized by points of the above mentioned curve is constructed. As a by-product, we obtain a representation of L(n) in terms of a finite number of generators and relations, which may be of independent interest.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
