scholarly journals A Generalized Construction of Calabi-Yau Models and Mirror Symmetry

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Per Berglund ◽  
Tristan Hubsch
Keyword(s):  
Sigma Models ◽  
General Class ◽  
Mirror Symmetry ◽  
Original Work ◽  
Convex Polytopes ◽  
Toric Varieties ◽  
Linear Sigma Models ◽  
Calabi Yau Manifolds

We extend the construction of Calabi-Yau manifolds to hypersurfaces in non-Fano toric varieties, requiring the use of certain Laurent defining polynomials, and explore the phases of the corresponding gauged linear sigma models. The associated non-reflexive and non-convex polytopes provide a generalization of Batyrev’s original work, allowing us to construct novel pairs of mirror models. We showcase our proposal for this generalization by examining Calabi-Yau hypersurfaces in Hirzebruch n-folds, focusing on n=3,4 sequences, and outline the more general class of so-defined geometries.

GEOMETRICAL DERIVATION OF THE FADDEEV-POPOV ANSATZ

1989 ◽  
Vol 04 (24) ◽  
pp. 2397-2407 ◽  
Author(s):  
P. ELLICOTT ◽  
G. KUNSTATTER ◽  
D.J. TOMS
Keyword(s):  
Invariant Measure ◽  
Sigma Models ◽  
Configuration Space ◽  
Effective Action ◽  
General Class ◽  
Gauge Theories ◽  
Yang Mills ◽  
Linear Sigma Models ◽  
Supersymmetric Theories

A geometrical derivation of the Faddeev-Popov measure is presented. This derivation is valid in any gauge for a general class of gauge theories, including Yang-Mills theory, gravitation and non-linear sigma models, and can easily be generalized to include supersymmetric theories. We stress the role of a non-trivial, finite contribution to the effective action from the invariant measure on the orbit over each point in the physical configuration space.

scholarly journals Supersymmetric black rings and non-linear sigma models

2010 ◽  
Vol 829 (1-2) ◽  
pp. 161-175 ◽  
Author(s):  
Yi-Xin Chen ◽  
Yong-Qiang Wang
Keyword(s):  
Sigma Models ◽  
Black Rings ◽  
Non Linear ◽  
Linear Sigma Models

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

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.

scholarly journals Phase transitions in GLSMs and defects

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.

scholarly journals Loop calculations in quantum-mechanical non-linear sigma models

1995 ◽  
Vol 446 (1-2) ◽  
pp. 211-222 ◽  
Author(s):  
Jan de Boer ◽  
Bas Peeters ◽  
Kostas Skenderis ◽  
Peter van Nieuwenhuizen
Keyword(s):  
Sigma Models ◽  
Quantum Mechanical ◽  
Non Linear ◽  
Linear Sigma Models

SUPERSYMMETRIC TENSOR GAUGE THEORIES

1989 ◽  
Vol 04 (14) ◽  
pp. 1343-1353 ◽  
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.

scholarly journals On D-branes from gauged linear sigma models

2001 ◽  
Vol 593 (1-2) ◽  
pp. 155-182 ◽  
Author(s):  
Suresh Govindarajan ◽  
T. Jayaraman ◽  
Tapobrata Sarkar
Keyword(s):  
Sigma Models ◽  
Linear Sigma Models
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