Heisenberg groups and noncommutative fluxes

By D. Freed, G. Moore, G. Segal. 2006

169 citations recorded by the source corpus.

Abstract We develop a group-theoretical approach to the formulation of generalized abelian gauge theories, such as those appearing in string theory and M-theory. We explore several applications of this approach. First, we show that there is an uncertainty relation which obstructs simultaneous measurement of electric and magnetic flux when torsion fluxes are included. Next, we show how to define the Hilbert space of a self-dual field. The Hilbert space is Z 2 -graded and we show that, in general, self-dual theories (including the RR fields of string theory) have fermionic sectors. We indicate how rational conformal field theories associated to the two-dimensional Gaussian model generalize to (4k + 2)-dimensional conformal field theories. When our ideas are applied to the RR fields of string theory we learn that it is impossible to measure the K-theory class of a RR field. Only the reduction modulo torsion can be measured.

Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f857b04ac998bae9ef204395e0befc3562476d7a

How researchers see this paper

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

In Nuclear and High Energy Physics

1. N. Seiberg
2. D. Gaiotto
3. G. Moore
4. E. Witten
5. A. Kapustin
6. F. Benini
7. Brian Willett
8. Tom Rudelius

In Statistical and Nonlinear Physics

1. G. Moore
2. N. Seiberg
3. D. Gaiotto
4. E. Witten
5. A. Kapustin
6. Frederik Denef
7. Tom Rudelius
8. Brian Willett

Citations in the corpus

• Generalized global symmetries (2014, background): “As in [21, 22], these operators satisfy a central extension of Z2 × Z2; i.”
• Split states, entropy enigmas, holes and halos (2007, background): “In this case one cannot simultaneously specify the electric and magnetic flux sectors on the D6 brane, and in fact, the ground states of the theory form a representation of the Heisenberg group extension of H(2) tors(X; Z) × H 5 tors(X; Z) defined by the torsion pairing [120, 121].”
• Anomalies in the space of coupling constants and their dynamical applications II (2019, unknown): “For another expository introduction, see [70].”
• On the Defect Group of a 6D SCFT (2015, background): “4) In more practical terms, to any given element h ∈ H(3)(M6, C), we can assign a corresponding quantum flux Φ(h) ∈ H(3)(M6, C) [43].”
• The Uncertainty of Fluxes (2006, background): “A companion paper [ FMS ] presents our ideas and fleshes out the examples in a more physical style.”
• Coupling a QFT to a TQFT and duality (2014, background): “The object one gets in this way is called a Deligne-Beilinson cocycle or a Cheeger-Simons differential character (see [25-28] for reviews aimed at physicists).”