Discrete Torsion

By E. Sharpe. 2000

161 citations recorded by the source corpus.

In this article we explain discrete torsion. Put simply, discrete torsion is the choice of orbifold group action on the B field. We derive the classification H 2 (Γ , U (1)), we derive the twisted sector phases appearing in string loop partition functions, we derive M. Douglas’s description of discrete torsion for D-branes in terms of a projective representation of the orbifold group, and we outline how the results of Vafa-Witten fit into this framework. In addition, we observe that additional degrees of freedom (known as shift orbifolds) appear in describing orbifold group actions on B fields, in addition to those classified by H 2 (Γ , U (1)), and explain how these degrees of freedom appear in terms of twisted sector contributions to partition functions and in terms of orbifold actions on D-brane worldvolumes. This paper represents a technically-simplified version of prior papers by the author on discrete torsion. We repeat here technically simplified versions of results from those papers, and have included some new material.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4fb5d5572b5b8d09a8d932c67d6cb324dc7fd4ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. A. Hanany
2. Yang-Hui He
3. Bo Feng
4. Paul D. Johnson
5. A. Libgober
6. K. Behrend
7. P. Xu
8. Alberto Zaffaroni

In Mathematical Physics

1. Yang-Hui He
2. M. Becker
3. A. Hanany
4. Bo Feng
5. P. Green
6. K. Behrend
7. E. Sharpe
8. Paul D. Johnson

In Nuclear and High Energy Physics

1. A. Hanany
2. Yang-Hui He
3. Bo Feng
4. P. Kovtun
5. M. Unsal
6. P. Green
7. M. Becker
8. K. Becker

Citations in the corpus

• Gapless Topological Phases and Symmetry-Enriched Quantum Criticality (2019, unknown): “[45] Eric Sharpe, “Discrete torsion,” Phys.”
• Equivariant Gromov-Witten theory of one dimensional stacks (2009, background): “ the mathematical literature cited above reserves the term “discrete torsion” for twisting by an element in H2(G,S1), the physics literature appears to use it to reference any such twisting: see e.g. [Sha]. These twistings should be understood as an extended and orbifold version of the physical noti”
• Volume independence in large Nc QCD-like gauge theories (2007, background): “In quiver gauge theories, one may also consider theory-space enlarging projections based on non-Abelian, or non-freely acting, symmetry groups [36].”
• Elliptic genera, real algebraic varieties and quasi-Jacobi forms (2009, background): “The chiral complex for orbifolds was constructed in [22] and the extension of (1-16) to orbifolds (with discrete torsion) is discussed in [39].”
• Notes on generalized global symmetries in QFT (2015, unknown): “[29], discrete torsion arises from choices”
• Differentiable stacks and gerbes (2006, background): “Motivation comes from string theory in which “gerbes with connections” appear naturally [13, 16, 23, 41].”
• Counting gauge invariants: The Plethystic program (2007, background): “J H E P 0 3 ( 2 0 0 7 ) 0 9 0 the situation is more interesting and the discrete-torsion and the corresponding Schur multipliers and covering groups have been computed and classified in [32].”
• Compactifications of heterotic strings on non-Kähler complex manifolds II (2003, background): “See [47], [48], and [49] for discussions of these subtleties in the case of discrete torsion, described as a group action on the B field.”