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## TOPOLOGICAL SIGMA MODELS

*Marcos Mariño*

### in Chern-Simons Theory, Matrix Models, and Topological Strings

- Published in print:
- 2005
- Published Online:
- September 2007
- ISBN:
- 9780198568490
- eISBN:
- 9780191717604
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198568490.003.0003
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology

String theory can be regarded, at the algebraic level, as a two-dimensional conformal field theory coupled to two-dimensional gravity. When the conformal field theory is also a topological field ... More

## Integrability in sigma-models

*K. Zarembo*

### in Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School: Volume 106, June 2016

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780198828150
- eISBN:
- 9780191866937
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828150.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The following topics are covered in this chapter: (1) Homogeneous spaces, (2) Classical integrability of sigma-models in two dimensions, (3) Topological terms, (4) Background-field method and ... More

## Integrability in 2D fields theory/sigma-models

*Sergei L. Lukyanov and Alexander B. Zamolodchikov*

### in Integrability: From Statistical Systems to Gauge Theory: Lecture Notes of the Les Houches Summer School: Volume 106, June 2016

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780198828150
- eISBN:
- 9780191866937
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198828150.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This is a two-part course about the integrability of two-dimensional non-linear sigma models (2D NLSM). In the first part general aspects of classical integrability are discussed, based on the O(3) ... More

## Interacting boson systems

*Xiao-Gang Wen*

### in Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons

- Published in print:
- 2007
- Published Online:
- February 2010
- ISBN:
- 9780199227259
- eISBN:
- 9780191713019
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199227259.003.03
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter introduces a quantum field theory for interacting boson systems. It develops a mean-field theory to study the superfluid phase. A path integral formulation is then developed to re-derive ... More

## Dynamical Mean-field Theories of Correlation and Disorder

*E. Miranda and V. Dobrosavljević*

### in Conductor-Insulator Quantum Phase Transitions

- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199592593
- eISBN:
- 9780191741050
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199592593.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter provides a review of recently-developed Dynamical Mean-Field Theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. The chapter first ... More

## Quantum field theory: Asymptotic safety

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0015
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 15 examines the conditions under which it is possible to define renormalized quantum field theories (QFTs) consistent on all scales (a property not necessary for effective QFTs and not shared ... More

## O(N) vector model in the ordered phase: Goldstone modes

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0010
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 10 examines the case of the spontaneous breaking of a continuous symmetry. When there is spontaneous symmetry breaking, the correlation length diverges at all temperatures in the ordered ... More

## Quantum field theory: An effective theory

*Jean Zinn-Justin*

### in From Random Walks to Random Matrices

- Published in print:
- 2019
- Published Online:
- August 2019
- ISBN:
- 9780198787754
- eISBN:
- 9780191829840
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198787754.003.0008
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

Chapter 8 discusses effective field theory. This concept is inspired by the theory of critical phenomena in statistical physics and based on renormalization group ideas. The basic idea behind ... More

## Statistical Mechanics and Quantum Field Theory

*Hans-Peter Eckle*

### in Models of Quantum Matter: A First Course on Integrability and the Bethe Ansatz

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780199678839
- eISBN:
- 9780191878589
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199678839.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

The connection between statistical mechanics on the one side and quantum mechanics and quantum field theory on the other side is based on the analogy between thermal and quantum fluctuations. ... More

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