Paper · Apr 19, 2018

On dual description of the deformed sigma model

A. V. Litvinov, L. A. Spodyneiko

hep-tharXiv:1804.07084v4
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Abstract

We study dual strong coupling description of integrability-preserving deformation of the sigma model. Dual theory is described by a coupled theory of Dirac fermions with four-fermion interaction and bosonic fields with exponential interactions. We claim that both theories share the same integrable structure and coincide as quantum field theories. We construct a solution of Ricci flow equation which behaves in the UV as a free theory perturbed by graviton operators and show that it coincides with the metric of the deformed sigma-model after duality transformation.

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Submitted
Apr 19, 2018
Last revised
Aug 7, 2018 (v4)
Subjects
hep-th, math-ph
DOI
10.1007/JHEP11(2018)139
Ricci flowPhysics

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  1. On dual regime in Yang-Baxter deformed sigma models

    Alexey Bychkov and Alexey Litvinov

    Topics Physics · Same author A. V. Litvinov · Shared terms “sigma model”, “deformed”, “bosonic fields”

  2. Classical and quantum integrable sigma models. Ricci flow, "nice duality" and perturbed rational conformal field theories

    Vladimir Fateev

    Topics Physics · Shared terms “sigma model”, “field theory”, “deformed”

  3. Ricci Flow from the Renormalization of Nonlinear Sigma Models in the Framework of Euclidean Algebraic Quantum Field Theory

    Mauro Carfora, Claudio Dappiaggi, Nicolò Drago et al.

    Topics Physics · Shared terms “sigma model”, “quantum field”, “field theory”

  4. Flag manifold sigma models: spin chains and integrable theories

    Ian Affleck, Dmitri Bykov and Kyle Wamer

    Topics Physics · Shared terms “sigma model”, “deformed”, “integrable”

  5. Sigma models as Gross-Neveu models

    Dmitri Bykov

    Topics Physics · Shared terms “sigma model”, “integrable”

  6. Integrable 2d sigma models: quantum corrections to geometry from RG flow

    Ben Hoare, Nat Levine and Arkady A. Tseytlin

    Topics Physics · Shared terms “sigma model”, “integrable”, “coupling”

  7. Conformal invariance from scale invariance in non-linear sigma models

    Yu Nakayama

    Topics Physics · Shared terms “sigma model”, “quantum field”, “field theory”

  8. Integrability and RG flow in 2d sigma models

    Nat Levine

    Topics Physics · Shared terms “sigma model”, “integrability”, “integrable”

Read around it

Background reading

The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.

Ricci flow Hamilton's Ricci flow evolves a Riemannian metric by minus twice its Ricci curvature. It is a nonlinear heat equation for geometry: it spreads… Start with: Three-manifolds with positive Ricci curvature (Hamilton, 1982) Physics Ricci flow first appeared in physics, as the leading-order renormalization-group flow of the string sigma model (Friedan, 1980). Start with: Nonlinear Models in 2+ε Dimensions (Friedan, 1980)

In the guidebook

  1. 5A.5
    Uniformization and the Two-Dimensional Ricci FlowBook 5A · Complex Analysis and Conformal Geometry

    Constant-curvature metrics on surfaces, and Ricci flow as a heat equation for the conformal factor.

  2. 10A.12
    Curve Shortening and Minimal DiscsBook 10A · Three-Manifolds and Geometrization

    How loops shrink under curvature, how the discs they bound lose area, and Perelman's extinction estimate.

  3. 11A.1
    The Equation and Its First SolutionsBook 11A · The Ricci Flow: Existence and Maximum Principles

    A heat equation for the metric: spheres, cylinders and scaling.