scholarly journals Homological classification of topological terms in sigma models on homogeneous spaces

2018 ◽  
Vol 2018 (9) ◽  
Author(s):  
Joe Davighi ◽  
Ben Gripaios
Keyword(s):  
Sigma Models ◽  
Homogeneous Spaces ◽  
Homological Classification

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.

Scale invariant sigma models on homogeneous spaces

1987 ◽  
Vol 194 (1) ◽  
pp. 69-74 ◽  
Author(s):  
E. Guadagnini ◽  
M. Martellini ◽  
M. Mintchev
Keyword(s):  
Sigma Models ◽  
Homogeneous Spaces ◽  
Scale Invariant

scholarly journals Integrability in sigma-models

2019 ◽  
pp. 205-247 ◽  
Author(s):  
K. Zarembo
Keyword(s):  
Sigma Models ◽  
Homogeneous Spaces ◽  
Beta Function ◽  
Background Field ◽  
Field Method ◽  
Two Dimensions ◽  
S Matrix ◽  
Background Field Method ◽  
Coset Models

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 beta-function, (5) S-matrix bootstrap in the O(N) model, (6) Supersymmetric coset models and strings on AdS(d) x X.

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