Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings

Journal Article · Fri Jan 28 04:00:00 EST 2005 · Nuclear Physics B

DOI:https://doi.org/10.1016/j.nuclphysb.2005.02.035· OSTI ID:964004

Aganagic, Mina; Ooguri, Hirosi; Saulina, Natalia; Vafa, Cumrun

We count the number of bound states of BPS black holes on local Calabi-Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang-Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e^-N), Z_BH is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The sub-leading chiral blocks involve topological string amplitudes with D-brane insertions at 2g-2 points on the Riemann surface analogous to the Omega points in the large N 2d Yang-Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c=1 non-critical string at the self-dual radius.

• Research Organization: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
• Sponsoring Organization: Physics Division
• DOE Contract Number: AC02-05CH11231
• OSTI ID: 964004
• Report Number(s): LBNL-56688
• Journal Information: Nuclear Physics B, Journal Name: Nuclear Physics B
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
analytic properties
black hole
BPS
dimension
2
expansion 1/N
field theory
deformation
field theory
topological
gauge field theory
Yang-Mills
membrane model
D-brane
partition function
string model