Dual pairs of gauged linear sigma models and derived equivalences of Calabi–Yau threefolds

N=(0,2) heterotic string theories on Calabi–Yau spaces are considered based on linear sigma approaches. We construct (0,2) sigma models on complete intersection Calabi–Yau spaces, ℳ, realized in a product of weighted projective spaces. The definition of the associating vector bundle V over ℳ is given. These models are formulated as the IR limits of (0,2) U (1)N gauged linear sigma models. Examining their phase structures, we observe that there are hybrid phases where one cannot intrinsically distinguish between the defining polynomials of the Calabi–Yau space ℳ and those of the gauge bundle V. Thus we construct dual pairs of two (0,2) Calabi–Yau sigma models which are isomorphic in their hybrid phases. In addition, generalizing the gauge bundle into the direct sum of bundles, we study the duality of (0,2) string vacua.

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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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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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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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Loop calculations in quantum-mechanical non-linear sigma models

Nuclear Physics B ◽

10.1016/0550-3213(95)00241-j ◽

1995 ◽

Vol 446 (1-2) ◽

pp. 211-222 ◽

Cited By ~ 43

Author(s):

Jan de Boer ◽

Bas Peeters ◽

Kostas Skenderis ◽

Peter van Nieuwenhuizen

Keyword(s):

Sigma Models ◽

Quantum Mechanical ◽

Non Linear ◽

Linear Sigma Models

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SUPERSYMMETRIC TENSOR GAUGE THEORIES

Modern Physics Letters A ◽

10.1142/s0217732389001532 ◽

1989 ◽

Vol 04 (14) ◽

pp. 1343-1353 ◽

Cited By ~ 16

Author(s):

T.E. CLARK ◽

C.-H. LEE ◽

S.T. LOVE

Keyword(s):

Gauge Theory ◽

Gauge Symmetry ◽

Sigma Models ◽

Gauge Field ◽

Gauge Theories ◽

Symmetric Tensor ◽

Global Symmetry ◽

Invariant Action ◽

Symmetry Transformations ◽

Linear Sigma Models

The supersymmetric extensions of anti-symmetric tensor gauge theories and their associated tensor gauge symmetry transformations are constructed. The classical equivalence between such supersymmetric tensor gauge theories and supersymmetric non-linear sigma models is established. The global symmetry of the supersymmetric tensor gauge theory is gauged and the locally invariant action is obtained. The supercurrent on the Kähler manifold is found in terms of the supersymmetric tensor gauge field.

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