The chiral de Rham complex and quantum non-linear sigma models

2011 ◽  
Vol 216 (1) ◽  
pp. 241-242
Author(s):  
J. Källén
Keyword(s):  
Sigma Models ◽  
De Rham Complex ◽  
Rham Complex ◽  
Non Linear ◽  
De Rham ◽  
Linear Sigma Models

scholarly journals Non-linear sigma models via the chiral de Rham complex

2009 ◽  
Vol 13 (4) ◽  
pp. 1221-1254 ◽  
Author(s):  
Joel Ekstrand ◽  
Reimundo Heluani ◽  
Johan Källén ◽  
Maxim Zabzine
Keyword(s):  
Sigma Models ◽  
De Rham Complex ◽  
Rham Complex ◽  
Non Linear ◽  
De Rham ◽  
Linear Sigma Models

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 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

scholarly journals Integral calculus on quantum exterior algebras

2014 ◽  
Vol 11 (04) ◽  
pp. 1450026 ◽  
Author(s):  
Serkan Karaçuha ◽  
Christian Lomp
Keyword(s):  
Differential Calculus ◽  
Polynomial Algebra ◽  
Exterior Algebra ◽  
Integral Calculus ◽  
De Rham Complex ◽  
Integral Forms ◽  
Rham Complex ◽  
De Rham ◽  
Quantum Polynomial

Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.

scholarly journals Chiral de Rham Complex over Locally Complete Intersections

2015 ◽  
Vol 15 (2) ◽  
pp. 353-372
Author(s):  
Fyodor Malikov ◽  
Vadim Schechtman
Keyword(s):  
Complete Intersections ◽  
De Rham Complex ◽  
Rham Complex ◽  
De Rham
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