scholarly journals The evaluation map in field theory, sigma-models and strings?II

1988 ◽  
Vol 114 (3) ◽  
pp. 381-437 ◽  
Author(s):  
L. Bonora ◽  
P. Cotta-Ramusino ◽  
M. Rinaldi ◽  
J. Stasheff
Keyword(s):  
Field Theory ◽  
Sigma Models

scholarly journals Smooth functorial field theories from B-fields and D-branes

2021 ◽  
Vol 16 (1) ◽  
pp. 75-153
Author(s):  
Severin Bunk ◽  
Konrad Waldorf
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Lagrangian Approach ◽  
Field Theories ◽  
Open Strings ◽  
Homotopy Invariant ◽  
Target Manifold ◽  
Definition Of ◽  
Smooth Map

AbstractIn the Lagrangian approach to 2-dimensional sigma models, B-fields and D-branes contribute topological terms to the action of worldsheets of both open and closed strings. We show that these terms naturally fit into a 2-dimensional, smooth open-closed functorial field theory (FFT) in the sense of Atiyah, Segal, and Stolz–Teichner. We give a detailed construction of this smooth FFT, based on the definition of a suitable smooth bordism category. In this bordism category, all manifolds are equipped with a smooth map to a spacetime target manifold. Further, the object manifolds are allowed to have boundaries; these are the endpoints of open strings stretched between D-branes. The values of our FFT are obtained from the B-field and its D-branes via transgression. Our construction generalises work of Bunke–Turner–Willerton to include open strings. At the same time, it generalises work of Moore–Segal about open-closed TQFTs to include target spaces. We provide a number of further features of our FFT: we show that it depends functorially on the B-field and the D-branes, we show that it is thin homotopy invariant, and we show that it comes equipped with a positive reflection structure in the sense of Freed–Hopkins. Finally, we describe how our construction is related to the classification of open-closed TQFTs obtained by Lauda–Pfeiffer.

Integrability in 2D fields theory/sigma-models

2019 ◽  
pp. 248-318
Author(s):  
Sergei L. Lukyanov ◽  
Alexander B. Zamolodchikov
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Field Theories ◽  
Two Dimensional ◽  
Conformal Field ◽  
Zero Curvature ◽  
Basic Facts ◽  
Linear Sigma Models ◽  
General Aspects

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) and O(4) sigma-models and the field theories related to them. The second part is devoted to the quantum 2D NLSM. Among the topics considered are: basic facts of conformal field theory, zero-curvature representations, integrals of motion, one-loop renormalizability of 2D NLSM, integrable structures in the so-called cigar and sausage models, and their RG flows. The text contains a large number of exercises of varying levels of difficulty.

scholarly journals CAUSAL TRANSFORMATION OF GÖDEL-TYPE SPACETIMES IN CONFORMAL FIELD THEORY

2010 ◽  
Vol 25 (34) ◽  
pp. 2873-2884 ◽  
Author(s):  
PAWEL GUSIN
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Sigma Models ◽  
Closed Timelike Curves ◽  
Conformal Field

The Gödel-type metrics are considered as backgrounds of the sigma-models. In the conformal field theory such backgrounds are deformed by the exactly marginal operators. We examine, how the closed timelike curves (CTCs) transform under such deformations.

scholarly journals Classical boundary field theory of Jacobi sigma models by Poissonization

2021 ◽  
Author(s):  
Ion Vancea
Keyword(s):  
Field Theory ◽  
Phase Space ◽  
Sigma Models ◽  
Sigma Model ◽  
Classical Field Theory ◽  
Classical Field ◽  
Second Order ◽  
Contact Manifolds ◽  
Boundary Field ◽  
Classical Boundary

In this paper, we are going to construct the classical field theory on the boundary of the embedding of \mathbb{R} \times S^{1}ℝ×S1 into the manifold MM by the Jacobi sigma model. By applying the poissonization procedure and by generalizing the known method for Poisson sigma models, we express the fields of the model as perturbative expansions in terms of the reduced phase space of the boundary. We calculate these fields up to the second order and illustrate the procedure for contact manifolds.

scholarly journals Non-abelian fermionic T-duality in supergravity

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Lev Astrakhantsev ◽  
Ilya Bakhmatov ◽  
Edvard T. Musaev
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Alternative Treatment ◽  
Killing Spinors ◽  
Transformation Rules ◽  
Double Field Theory ◽  
Field Transformation ◽  
Complex Valued

Abstract Field transformation rules of the standard fermionic T-duality require fermionic isometries to anticommute, which leads to complexification of the Killing spinors and results in complex valued dual backgrounds. We generalize the field transformations to the setting with non-anticommuting fermionic isometries and show that the resulting backgrounds are solutions of double field theory. Explicit examples of non-abelian fermionic T-dualities that produce real backgrounds are given. Some of our examples can be bosonic T-dualized into usual supergravity solutions, while the others are genuinely non-geometric. Comparison with alternative treatment based on sigma models on supercosets shows consistency.

scholarly journals Fluxes in exceptional field theory and threebrane sigma-models

2019 ◽  
Vol 2019 (5) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Larisa Jonke ◽  
Dieter Lüst ◽  
Richard J. Szabo
Keyword(s):  
Field Theory ◽  
Sigma Models

scholarly journals Double field theory and membrane sigma-models

2018 ◽  
Vol 2018 (7) ◽  
Author(s):  
Athanasios Chatzistavrakidis ◽  
Larisa Jonke ◽  
Fech Scen Khoo ◽  
Richard J. Szabo
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Double Field Theory

scholarly journals COMMENTS ABOUT THE GEOMETRY OF NONLINEAR SIGMA MODELS

1987 ◽  
Vol 02 (06) ◽  
pp. 1763-1772 ◽  
Author(s):  
ROBERT COQUEREAUX
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Sigma Models ◽  
Effective Action ◽  
Quantum Field ◽  
Geometrical Meaning ◽  
Perturbative Quantum ◽  
Perturbative Quantum Field Theory ◽  
The One ◽  
Nonlinear Sigma Models

Geometrical aspects of several classes of σ models are studied. The geometrical meaning of perturbative quantum field theory is discussed in the content of nonlinear σ models. Results on the one-loop effective action are recovered and generalized.

scholarly journals Trace and chiral anomalies in string and ordinary field theory from Feynman diagrams for non-linear sigma models

1998 ◽  
Vol 518 (1-2) ◽  
pp. 424-454 ◽  
Author(s):  
Agapitos Hatzinikitas ◽  
Koenraad Schalm ◽  
Peter van Nieuwenhuizen
Keyword(s):  
Field Theory ◽  
Sigma Models ◽  
Feynman Diagrams ◽  
Non Linear ◽  
Linear Sigma Models
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