Lie Algebra Expansion and Integrability in Superstring Sigma-Models

Abstract

Lie algebra expansion is a technique to generate new Lie algebras from a given one. In this paper, we apply the method of Lie algebra expansion to superstring $\sigma$-models with a ${\mathbb{Z}}_4$ coset target space. By applying the Lie algebra expansion to the isometry algebra, we obtain different $\sigma$-models, where the number of dynamical fields can change. We reproduce and extend in a systematic way actions of some known string regimes (flat space, BMN and non-relativistic in AdS${}_5\times$S${}^5$). We define a criterion for the algebra truncation such that the equations of motion of the expanded action of the new $\sigma$-model are equivalent to the vanishing curvature condition of the Lax connection obtained by expanding the Lax connection of the initial model.

32 pages, LaTeX; references added, matching the published version

References in corpus (62)

• Large N Field Theories, String Theory and Gravity
• Review of AdS/CFT Integrability: An Overview
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• Type IIB superstring action in AdS_5 x S^5 background
• Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background
• The su(2|2) Dynamic S-Matrix
• Foundations of the AdS_5 x S^5 Superstring. Part I
• An integrable deformation of the AdS_5 x S^5 superstring action
• Hall Viscosity and Electromagnetic Response
• Non-Relativistic Closed String Theory
• Green-Schwarz action for Type IIA strings on $Ad{S}_4\times C{P}^3$
• Superstrings on AdS_4 x CP^3 as a Coset Sigma-model
• Torsional Newton-Cartan Geometry and Lifshitz Holography
• Gauging the Carroll Algebra and Ultra-Relativistic Gravity
• Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography
• Non-Relativistic Superstrings: A New Soluble Sector of AdS_5xS^5
• Spacetime Symmetries of the Quantum Hall Effect
• Non-Relativistic Strings and Limits of the AdS/CFT Correspondence
• Action Principle for Newtonian Gravity
• Carroll versus Galilei Gravity
• Dynamics of Carroll Particles
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• Expanding Lie (super)algebras through abelian semigroups
• Nonrelativistic String Theory and T-Duality
• Strings on Semisymmetric Superspaces
• Non-Relativistic Gravity and its Coupling to Matter
• String Theory and String Newton-Cartan Geometry
• Newton-Hooke Algebras, Non-relativistic Branes and Generalized pp-wave Metrics
• Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction
• Non-relativistic strings and branes as non-linear realizations of Galilei groups
• Relating non-relativistic string theories
• Superstrings in AdS(2)xS(2)xT(6)
• Nonrelativistic String Theory in Background Fields
• From Super-AdS_5xS^5 Algebra to Super-pp-wave Algebra
• Expansions of algebras and superalgebras and some applications
• Dynamics of Carroll Strings
• Gravity between Newton and Einstein
• Spatially isotropic homogeneous spacetimes
• Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity
• Lie Algebra Expansions and Actions for Non-Relativistic Gravity
• An Integrability Primer for the Gauge-Gravity Correspondence: an Introduction
• On the Dressing Factors, Bethe Equations and Yangian Symmetry of Strings on AdS3 x S3 x T4
• An Action for Extended String Newton-Cartan Gravity
• Geometry and BMS Lie algebras of spatially isotropic homogeneous spacetimes
• Background Field Method for Nonlinear Sigma Models in Nonrelativistic String Theory
• Three-Dimensional Extended Newtonian (Super)Gravity
• Non-Relativistic Gravity Theory based on an Enlargement of the Extended Bargmann Algebra
• Nonrelativistic String Theory Sigma Model and Its Canonical Formulation
• Three-Dimensional Extended Lifshitz, Schrödinger and Newton-Hooke Supergravity
• Three-dimensional exotic Newtonian gravity with cosmological constant
• The S-matrix algebra of the AdS2 X S2 superstring
• Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions
• Nonrelativistic pulsating strings
• Generalized Galilean Algebras and Newtonian Gravity
• Non-relativistic String and D-branes on AdS_5 x S^5 from Semiclassical Approximation
• Three-Dimensional Higher-Order Schrödinger Algebras and Lie Algebra Expansions
• Massless $Ad{S}_2$ scattering and Bethe ansatz
• Extended gauge theory and gauged Free Differential Algebras
• Lax pairs for string Newton Cartan geometry
• Kinematical superspaces
• Note About Integrability of Non-Relativistic String
• Newton-Cartan $D0$ branes from $D1$ branes and integrability

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• Spin Matrix Theory String Backgrounds and Penrose Limits of AdS/CFT
• Non-relativistic three-dimensional supergravity theories and semigroup expansion method
• Three-dimensional Maxwellian Extended Newtonian gravity and flat limit
• Three-dimensional exotic Newtonian supergravity theory with cosmological constant
• Classical string solutions in Non-Relativistic AdS${}_5\times$S${}^5$: Closed and Twisted sectors
• Three-dimensional non-relativistic supergravity and torsion
• Coset space actions for nonrelativistic strings
• Extending the non-relativistic string AdS coset
• Non-relativistic string monodromies
• Three-dimensional Newtonian gravity with cosmological constant and torsion
• Light-Cone Gauge in Non-Relativistic AdS${}_5\times$S${}^5$ String Theory
• Constructing Non-Relativistic AdS${}_5$/CFT${}_4$ Holography
• Lie Algebra Expansions, Non-Relativistic Matter Multiplets and Actions
• A perturbative approach to the non-relativistic string spectrum