Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds

This chapter examines various ways to construct symplectic manifolds and submanifolds. It begins by studying blowing up and down in both the complex and the symplectic contexts. The next section is devoted to a discussion of fibre connected sums and describes Gompf’s construction of symplectic four-manifolds with arbitrary fundamental group. The chapter also contains an exposition of Gromov’s telescope construction, which shows that for open manifolds the h-principle rules and the inclusion of the space of symplectic forms into the space of nondegenerate 2-forms is a homotopy equivalence. The final section outlines Donaldson’s construction of codimension two symplectic submanifolds and explains the associated decompositions of the ambient manifold.

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Supersymmetric black rings and non-linear sigma models

Nuclear Physics B ◽

10.1016/j.nuclphysb.2009.12.008 ◽

2010 ◽

Vol 829 (1-2) ◽

pp. 161-175 ◽

Cited By ~ 1

Author(s):

Yi-Xin Chen ◽

Yong-Qiang Wang

Keyword(s):

Sigma Models ◽

Black Rings ◽

Non Linear ◽

Linear Sigma Models

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Massive hyper-Kähler sigma models and BPS domain walls

Physics of Atomic Nuclei ◽

10.1134/1.2121909 ◽

2005 ◽

Vol 68 (10) ◽

pp. 1634-1642 ◽

Cited By ~ 8

Author(s):

M. Arai ◽

M. Nitta ◽

N. Sakai

Keyword(s):

Sigma Models ◽

Domain Walls

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Quantum corrections to generic branes: DBI, NLSM, and more

Journal of High Energy Physics ◽

10.1007/jhep01(2021)159 ◽

2021 ◽

Vol 2021 (1) ◽

Author(s):

Garrett Goon ◽

Scott Melville ◽

Johannes Noller

Keyword(s):

Sigma Models ◽

Quantum Corrections ◽

Higher Dimensional ◽

Symmetry Properties ◽

Non Linear ◽

Quantum Action ◽

Manifest Covariance ◽

Linear Sigma Models ◽

Scalar Sector ◽

Explicit Comparison

Abstract We study quantum corrections to hypersurfaces of dimension d + 1 > 2 embedded in generic higher-dimensional spacetimes. Manifest covariance is maintained throughout the analysis and our methods are valid for arbitrary co-dimension and arbitrary bulk metric. A variety of theories which are prominent in the modern amplitude literature arise as special limits: the scalar sector of Dirac-Born-Infeld theories and their multi-field variants, as well as generic non-linear sigma models and extensions thereof. Our explicit one-loop results unite the leading corrections of all such models under a single umbrella. In contrast to naive computations which generate effective actions that appear to violate the non-linear symmetries of their classical counterparts, our efficient methods maintain manifest covariance at all stages and make the symmetry properties of the quantum action clear. We provide an explicit comparison between our compact construction and other approaches and demonstrate the ultimate physical equivalence between the superficially different results.

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

Journal of Homotopy and Related Structures ◽

10.1007/s40062-020-00272-2 ◽

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.

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Phase transitions in GLSMs and defects

Journal of High Energy Physics ◽

10.1007/jhep05(2021)006 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Ilka Brunner ◽

Fabian Klos ◽

Daniel Roggenkamp

Keyword(s):

Phase Transitions ◽

Boundary Conditions ◽

Sigma Models ◽

Domain Walls ◽

Two Dimensional ◽

Linear Sigma Models

Abstract In this paper, we construct defects (domain walls) that connect different phases of two-dimensional gauged linear sigma models (GLSMs), as well as defects that embed those phases into the GLSMs. Via their action on boundary conditions these defects give rise to functors between the D-brane categories, which respectively describe the transport of D-branes between different phases, and embed the D-brane categories of the phases into the category of D-branes of the GLSMs.

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Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures

Journal of High Energy Physics ◽

10.1007/jhep11(2020)173 ◽

2020 ◽

Vol 2020 (11) ◽

Author(s):

Athanasios Chatzistavrakidis ◽

Grgur Šimunić

Keyword(s):

Sigma Models ◽

Sigma Model ◽

Target Space ◽

Two Dimensional ◽

Courant Algebroids ◽

Dirac Structures ◽

Courant Algebroid ◽

Abelian Case ◽

Jacobi Manifolds ◽

Jacobi Structure

Abstract We study aspects of two-dimensional nonlinear sigma models with Wess-Zumino term corresponding to a nonclosed 3-form, which may arise upon dimensional reduction in the target space. Our goal in this paper is twofold. In a first part, we investigate the conditions for consistent gauging of sigma models in the presence of a nonclosed 3-form. In the Abelian case, we find that the target of the gauged theory has the structure of a contact Courant algebroid, twisted by a 3-form and two 2-forms. Gauge invariance constrains the theory to (small) Dirac structures of the contact Courant algebroid. In the non-Abelian case, we draw a similar parallel between the gauged sigma model and certain transitive Courant algebroids and their corresponding Dirac structures. In the second part of the paper, we study two-dimensional sigma models related to Jacobi structures. The latter generalise Poisson and contact geometry in the presence of an additional vector field. We demonstrate that one can construct a sigma model whose gauge symmetry is controlled by a Jacobi structure, and moreover we twist the model by a 3-form. This construction is then the analogue of WZW-Poisson structures for Jacobi manifolds.

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