Pohlmeyer reduction for superstrings in AdS space

Abstract

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS_5 x S^5 have been used recently in the study of classical Euclidean minimal surfaces for Wilson loops and some semiclassical three-point correlation functions. We find an action that leads to these reduced superstring equations. For example, for a bosonic string in AdS_n such an action contains a Liouville scalar part plus a K/K gauged WZW model for the group K=SO(n-2) coupled to another term depending on two additional fields transforming as vectors under K. Solving for the latter fields gives a non-abelian Toda model coupled to the Liouville theory. For n=5 we generalize this bosonic action to include the S^5 contribution and fermionic terms. The corresponding reduced model for the AdS_2 x S^2 truncation of the full AdS_5 x S^5 superstring turns out to be equivalent to N=2 super Liouville theory. Our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in AdS_n x S^1 and superstrings in AdS_5 x S^5. This new action may be useful as a starting point for possible quantum generalizations or deformations of the classical Pohlmeyer-reduced theory. We give examples of simple extrema of this reduced superstring action which represent strings moving in the AdS_5 part of the space. Expanding near these backgrounds we compute the corresponding fluctuation spectra and show that they match the spectra found in the original superstring theory.

54 pages; v2: 57 pages, added various comments, references and a new subsection on N=2 super Liouville theory as reduced model for the AdS2 x S2 superstring; v3: reference added and typo corrected

References in corpus (40)

• Review of AdS/CFT Integrability: An Overview
• A semi-classical limit of the gauge/string correspondence
• Type IIB superstring action in AdS_5 x S^5 background
• Giant Magnons
• Liouville Field Theory -- A decade after the revolution
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• A WZW model based on a non-semi-simple group
• Superstring Theory on AdS_2 x S^2 as a Coset Supermanifold
• Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model
• Light-cone Superstring in AdS Space-time
• Quantum Deformations of the One-Dimensional Hubbard Model
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• The Symmetric Space and Homogeneous sine-Gordon Theories
• Strong-coupling expansion of cusp anomaly and gluon amplitudes from quantum open strings in AdS_5 x S^5
• Exciting the GKP string at any coupling
• Lagrangian Formulation of Symmetric Space sine-Gordon Models
• Nonsemisimple Sugawara Constructions
• Superstrings in AdS(2)xS(2)xT(6)
• Towards the quantum S-matrix of the Pohlmeyer reduced version of AdS_5 x S^5 superstring theory
• Quantum scattering of charged solitons in the complex sine-Gordon model
• On reduced models for superstrings on AdS_n x S^n
• Solitons and AdS String Solutions
• The Topological G/G WZW Model in the Generalized Momentum Representation
• An action variable of the sine-Gordon model
• Exact four dimensional string solutions and Toda-like sigma models from `null-gauged' WZNW theories
• Notes on Euclidean Wilson loops and Riemann Theta functions
• Black Holes from Non-Abelian Toda Theories
• $G/G$--Topological Field Theories by Cosetting $G_k$
• A nonlocal Poisson bracket of the sine-Gordon model
• Massive Integrable Soliton Theories
• Pohlmeyer-reduced form of string theory in AdS_5 x S^5: semiclassical expansion
• The Classical Trigonometric r-Matrix for the Quantum-Deformed Hubbard Chain
• Non Abelian Toda Theory : A Completely Integrable Model for Strings on a Black Hole Background
• Luescher formula for GKP string
• Integrability of a family of quantum field theories related to sigma models
• A lattice Poisson algebra for the Pohlmeyer reduction of the AdS_5 x S^5 superstring
• Superstrings in AdS in light cone gauge
• One-loop corrections to AdS_5 x S^5 superstring partition function via Pohlmeyer reduction
• Two-loop corrections to partition function of Pohlmeyer-reduced theory for AdS_5 x S^5 superstring
• Gravitational dressing of massive soliton theories

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