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200
Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
, 2007
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Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories
, 1996
"... These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying ..."
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Cited by 139 (13 self)
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These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings
, 2004
"... We count the number of bound states of BPS black holes on local Calabi-Yau threefolds 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 h ..."
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Cited by 99 (11 self)
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We count the number of bound states of BPS black holes on local Calabi-Yau threefolds 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), ZBH 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 Ω 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.
Supersymmetric Yang–Mills theory on a four-manifold
- Jour. Math. Phys
, 1994
"... By exploiting standard facts about N = 1 and N = 2 supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about ..."
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Cited by 88 (3 self)
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By exploiting standard facts about N = 1 and N = 2 supersymmetric Yang-Mills theory, the Donaldson invariants of four-manifolds that admit a Kahler metric can be computed. The results are in agreement with available mathematical computations, and provide a powerful check on the standard claims about supersymmetric Yang-Mills theory. In four-dimensional supersymmetric Yang-Mills theory formulated on flat R4, certain correlation functions are independent of spatial separation and are hence effectively computable by going to short distances. This is the basis for one of the most fruitful techniques for studying dynamics of those theories [1,2], and
Quantized Gauge Theory on the Fuzzy Sphere as Random
- Matrix Model, Nucl. Phys. B679
, 2004
"... Gauge theories provide the best known description of the fundamental forces in nature. At very short distances however, physics is not known, and it seems unlikely that spacetime is a perfect continuum down to arbitrarily small scales. Indeed, physicists have started to learn in recent years how to ..."
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Cited by 59 (16 self)
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Gauge theories provide the best known description of the fundamental forces in nature. At very short distances however, physics is not known, and it seems unlikely that spacetime is a perfect continuum down to arbitrarily small scales. Indeed, physicists have started to learn in recent years how to formulate field
Vector bundles on curves and generalized theta functions: recent results and open problems
- CAMBRIDGE UNIVERSITY PRESS
, 1995
"... The moduli spaces of vector bundles on a compact Riemann surface carry a natural line bundle, the determinant bundle. The sections of this line bundle and its multiples constitute a non-abelian generalization of the classical theta functions. New ideas coming from mathematical physics have shed a ..."
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Cited by 58 (3 self)
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The moduli spaces of vector bundles on a compact Riemann surface carry a natural line bundle, the determinant bundle. The sections of this line bundle and its multiples constitute a non-abelian generalization of the classical theta functions. New ideas coming from mathematical physics have shed a new light on these spaces of sections—allowing notably to compute their dimension (Verlinde’s formula). This survey paper is devoted to giving an overview of these ideas and of the most important recent results on the subject.
An analytic proof of the geometric quantization conjecture
- of GuilleminSternberg, Invent. Math 132
, 1998
"... Abstract. We present a direct analytic approach to the Guillemin-Sternberg conjecture [GS] that ‘geometric quantization commutes with symplectic reduction’, which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods a ..."
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Cited by 55 (8 self)
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Abstract. We present a direct analytic approach to the Guillemin-Sternberg conjecture [GS] that ‘geometric quantization commutes with symplectic reduction’, which was proved recently by Meinrenken [M1], [M2] and Vergne [V1], [V2] et al. Besides providing a new proof of this conjecture, our methods also lead immediately to further extensions in various contexts. Let M;x be a closed symplectic manifold such that there is a Hermitian line bundle L over M admitting a Hermitian connection rL with the prop-erty that ÿ1p
Lectures on curved beta-gamma systems, pure spinors, and anomalies
"... The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-linear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism an ..."
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Cited by 52 (3 self)
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The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-linear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism anomalies which we review. We analyze the curved betagamma system on the space of pure spinors, aiming to verify the consistency of Berkovits covariant superstring quantization. We demonstrate that under certain conditions both anomalies can be cancelled for the pure spinor sigma model, in which case one reproduces the old construction of B. Feigin and E. Frenkel.
