Dirac Charge Quantization and Generalized Differential Cohomology
By D. Freed. 2000
198 citations recorded by the source corpus.
The main new result here is the cancellation of global anomalies in the Type I superstring, with and without D-branes. Our argument here depends on a precise interpretation of the 2-form abelian gauge field using KO-theory; then the anomaly cancellation follows from a geometric form of the full Atiyah-Singer index theorem for families of Dirac operators. This is a refined version of the Green-Schwarz mechanism. It seems that a geometric interpretation of this mechanism-the cancellation of local and global fermion anomalies against local and global anomalies in the electric coupling of an abelian gauge field-always proceeds in a similar manner. For example, a previous paper with M. Hopkins (hep-th/0002027) explains the cancellation of anomalies in Type II with D-branes in these terms. The focal point of this paper is a general discussion about abelian gauge fields and Dirac charge quantization. Namely, we argue that quantization of charge is implemented in the functional integral by interpreting abelian gauge fields as cochains in a generalized differential cohomology theory. Our exposition includes elementary examples as well as examples from superstring theory. The mathematical underpinnings of differential cohomology are currently under development; we only give a sketch here. The anomaly cancellation in Type I depends on properties of a certain quadratic form in KO-theory, which we analyze in an appendix written jointly with M. Hopkins. In particular, the usual equation ``Tr R^2 = Tr F^2'' is refined to an equation in the KO-theory of spacetime.
Subfields: Mathematical Physics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/160429d165d15c7b5cad58e2caf123b351f41156
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Citations in the corpus
- Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory (2008, background): “(7)Such quadratic refinements frequently appear in the precise formulations of self-dual gauge theories [33, 34, 35, 36].”
- D-Brane Instantons and K-Theory Charges (2001, methodology): “Institute for Advanced Study Einstein Drive Princeton, New Jersey, 08540”
- Heisenberg groups and noncommutative fluxes (2006, background): “…im m ediate: 7 D e nition TheCheeger-Sim onsgroup ofdi erentialcharacters,denoted H ‘(M ),isthe subgroup ofallhom om orphism sfrom closed (‘ 1)-cyclesto U (1): H ‘(M ) Hom (Z‘ 1 (M );U (1)) (2:4) satisfying the following property: For each 2 H ‘(M ) there is a globally well-de ned F 2 ‘(M…”
- 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).”
- Framed BPS states (2010, unknown): “In the path integral of the abelian six-dimensional theory the sum over topological sectors is weighted by a quadratic refinement of the mod-two intersection form on H(3)(M6;Z) [39, 40, 41, 42].”
- Twisted Differential String and Fivebrane Structures (2009, methodology): “Introduction String theory and M-theory involve various higher gauge-fields, which are locally given by differential form fields of higher degree and which are globally modeled by higher bundles with connection (higher gerbes with connection, higher differential characters) [33] (cf.”
- Triples, Fluxes, and Strings (2001, methodology): “To be more precise, there is a local formulation of K-theory called differential K-theory that provides a precise characterization of the RR fields in terms of bundles with connections [79].”