(0,2) CALABI–YAU SIGMA MODELS AND THEIR DUALITY

1998 ◽  
Vol 13 (05) ◽  
pp. 779-796
Author(s):  
MAKOTO SAKAGUCHI
Keyword(s):  
Vector Bundle ◽  
Sigma Models ◽  
Complete Intersection ◽  
Heterotic String ◽  
Dual Pairs ◽  
Direct Sum ◽  
Phase Structures ◽  
Heterotic String Theories ◽  
Linear Sigma Models ◽  
Definition Of

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.

scholarly journals Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Svetlana Ermakova
Keyword(s):  
Vector Bundle ◽  
Complete Intersection ◽  
Finite Rank ◽  
Vector Bundles ◽  
Complete Intersections ◽  
Finite Codimension ◽  
Line Bundles ◽  
Direct Sum ◽  
Rank Vector

AbstractIn this article we establish an analogue of the Barth-Van de Ven-Tyurin-Sato theorem.We prove that a finite rank vector bundle on a complete intersection of finite codimension in a linear ind-Grassmannian is isomorphic to a direct sum of line bundles.

scholarly journals Algebraic Reduced Genus One Gromov–Witten Invariants for Complete Intersections in Projective Spaces

2019 ◽  
Author(s):  
Sanghyeon Lee ◽  
Jeongseok Oh
Keyword(s):  
Algebraic Geometry ◽  
Vector Bundle ◽  
Complete Intersection ◽  
Comparison Theorem ◽  
Euler Number ◽  
Projective Spaces ◽  
Complete Intersections ◽  
Dimension 2 ◽  
Definition Of ◽  
Genus One

Abstract In [ 17, 18], Zinger defined reduced Gromov–Witten (GW) invariants and proved a comparison theorem of standard and reduced genus one GW invariants for every symplectic manifold (with all dimension). In [ 3], Chang and Li provided a proof of the comparison theorem for quintic Calabi–Yau three-folds in algebraic geometry by taking a definition of reduced invariants as an Euler number of certain vector bundle. In [ 5], Coates and Manolache have defined reduced GW invariants in algebraic geometry following the idea by Vakil and Zinger in [ 14] and proved the comparison theorem for every Calabi–Yau threefold. In this paper, we prove the comparison theorem for every (not necessarily Calabi–Yau) complete intersection of Dimension 2 or 3 in projective spaces by taking a definition of reduced GW invariants in [ 5].

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 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.

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
Sign in / Sign up

Export Citation Format

Share Document