Conformal invariance and quantum integrability of sigma models on symmetric superspaces

Abstract

We consider two dimensional non linear sigma models on few symmetric superspaces, which are supergroup manifolds of coset type. For those spaces where one loop beta function vanishes, two loop beta function is calculated and is shown to be zero. Vanishing of beta function in all orders of perturbation theory is shown for the principal chiral models on group supermanifolds with zero Killing form. Sigma models on symmetric (super) spaces on supergroup manifold $G/H$ are known to be classically integrable. We investigate a possibility to extend an argument of absence of quantum anomalies in non local current conservation from non super case to the case of supergroup manifolds which are asymptotically free in one loop.

arXiv commentreferences added

References in corpus (23)

• Type IIB superstring action in AdS_5 x S^5 background
• Riemannian symmetric superspaces and their origin in random matrix theory
• The Dilatation Operator of N=4 Super Yang-Mills Theory and Integrability
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Exact spectra of conformal supersymmetric nonlinear sigma models in two dimensions
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• Spinning strings and integrable spin chains in the AdS/CFT correspondence
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• The GL(1|1) WZW model: From Supergeometry to Logarithmic CFT
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Supermanifolds, Rigid Manifolds and Mirror Symmetry
• Semiclassical Bethe Ansatz and AdS/CFT
• Non-local charges, Zm gradings and coset space actions
• Mirror Symmetry and Supermanifolds
• Conformal Fixed Points of Unidentified Gauge Theories
• Sigma-models having supermanifolds as target spaces
• Conformal Sigma-Models on Supercoset Targets
• Flat Currents of the Green-Schwarz Superstrings in AdS_5 x S^1 and AdS_3 x S^3 backgrounds
• The Exact S-Matrix for an osp(2|2) Disordered System
• Non-local charges and quantum integrability of sigma models on the symmetric spaces SO(2n)/SO(n)xSO(n) and Sp(2n)/Sp(n)xSp(n)
• Flux Vacua and Supermanifolds
• Quantum Strings and Bethe Equations

Cited by in corpus (23)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• Strings on Semisymmetric Superspaces
• Beta Function of k Deformed AdS_5 x S^5 String Theory
• Integrability of Type II Superstrings on Ramond-Ramond Backgrounds in Various Dimensions
• Free fermion resolution of supergroup WZNW models
• Boundary Spectra in Superspace Sigma-Models
• Conformal Current Algebra in Two Dimensions
• Superspace conformal field theory
• Takiff superalgebras and Conformal Field Theory
• Integrable sigma models and 2-loop RG flow
• The conformal current algebra on supergroups with applications to the spectrum and integrability
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
• First-principles derivation of the AdS/CFT Y-systems
• Cohomological Reduction of Sigma Models
• On the Spectrum of Superspheres
• Superspace Parafermions
• Non-chiral current algebras for deformed supergroup WZW models
• Spectra of Coset Sigma Models
• Yangian Superalgebras in Conformal Field Theory
• Differential operator realizations of superalgebras and free field representations of corresponding current algebras
• More on (gauged) WZW models over low-dimensional Lie supergroups and their integrable deformations
• Multi-parametric R-matrix for the sl(2|1) Yangian
• Deconfined quantum criticality with internal supersymmetry