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294
Localization of gauge theory on a foursphere and supersymmetric Wilson loops
, 2007
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Split States, Entropy Enigmas, Holes and Halos
, 2007
"... We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute e ..."
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Cited by 235 (22 self)
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We investigate degeneracies of BPS states of Dbranes on compact CalabiYau manifolds. We develop a factorization formula for BPS indices using attractor flow trees associated to multicentered black hole bound states. This enables us to study background dependence of the BPS spectrum, to compute explicitly exact indices of various nontrivial Dbrane systems, and to clarify the subtle relation of DonaldsonThomas invariants to BPS indices of stable D6D2D0 states, realized in supergravity as “hole halos. ” We introduce a convergent generating function for D4 indices in the large CY volume limit, and prove it can be written as a modular average of its polar part, generalizing the fareytail expansion of the elliptic genus. We show polar states are “split ” D6antiD6 bound states, and that the partition function factorizes accordingly, leading to a refined version of the OSV conjecture. This differs from the original conjecture in several aspects. In particular we obtain a nontrivial measure factor g −2 top e−K and find factorization requires a cutoff. We show that the main factor determining the cutoff and therefore the error is the existence of “swing states ” — D6 states which exist at large radius but do not form stable D6antiD6 bound states. We point out a likely breakdown of the OSV conjecture at small gtop (in the large background CY volume limit), due to the surprising phenomenon that for sufficiently large background Kähler moduli, a charge ΛΓ supporting single centered black holes of entropy ∼ Λ2S(Γ) also admits twocentered BPS black hole realizations whose entropy grows like Λ3 when Λ → ∞.
Quantization of Integrable Systems and Four Dimensional Gauge Theories
, 2009
"... We study four dimensional N = 2 supersymmetric gauge theory in the Ωbackground with the two dimensional N = 2 superPoincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimension ..."
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Cited by 114 (3 self)
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We study four dimensional N = 2 supersymmetric gauge theory in the Ωbackground with the two dimensional N = 2 superPoincare invariance. We explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional N = 2 theory. The εparameter of the Ωbackground is identified with the Planck constant, the twisted chiral ring maps to quantum Hamiltonians, the supersymmetric vacua are identified with Bethe states of quantum integrable systems. This four dimensional gauge theory in its low energy description has two dimensional twisted superpotential which becomes the YangYang function of the integrable system. We present the thermodynamicBetheansatz like formulae for these functions and for the spectra of commuting Hamiltonians following the direct computation in gauge theory. The general construction is illustrated at the examples of the manybody systems, such as the periodic Toda chain, the elliptic CalogeroMoser system, and their relativistic versions, for which we present a complete characterization of the L²spectrum. We very briefly discuss the quantization of Hitchin system.
Duality and defects in rational conformal field theory
, 2006
"... We study topological defect lines in twodimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We sh ..."
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Cited by 60 (24 self)
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We study topological defect lines in twodimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting onedimensional phase boundaries can be used to extract symmetries and orderdisorder dualities of the CFT. The case of central charge c = 4/5, for which there are two inequivalent world sheet phases corresponding to the tetracritical Ising model and the critical threestates
CONSTRUCTIBLE SHEAVES AND THE FUKAYA CATEGORY
, 2006
"... Abstract. Let Sh(X) be the triangulated dg category of bounded, constructible complexes of sheaves on a manifold X. Let TwFuk(T ∗ X) be the triangulated A∞category of twisted complexes in the Fukaya category of the cotangent bundle T ∗ X. We prove that Sh(X) embeds as an A∞subcategory of TwFuk(T ∗ ..."
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Cited by 42 (10 self)
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Abstract. Let Sh(X) be the triangulated dg category of bounded, constructible complexes of sheaves on a manifold X. Let TwFuk(T ∗ X) be the triangulated A∞category of twisted complexes in the Fukaya category of the cotangent bundle T ∗ X. We prove that Sh(X) embeds as an A∞subcategory of TwFuk(T ∗ X). Taking cohomology gives an embedding of the corresponding derived categories.
Mixed Hodge polynomials of character varieties
"... We calculate the Epolynomials of certain twisted GL(n,C)character varietiesMn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lietype GL(n,Fq) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geomet ..."
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Cited by 38 (9 self)
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We calculate the Epolynomials of certain twisted GL(n,C)character varietiesMn of Riemann surfaces by counting points over finite fields using the character table of the finite group of Lietype GL(n,Fq) and a theorem proved in the appendix by N. Katz. We deduce from this calculation several geometric results, for example, the value of the topological Euler characteristic of the associated PGL(n,C)character variety. The calculation also leads to several conjectures about the cohomology of Mn: an explicit conjecture for its mixed Hodge polynomial; a conjectured curious Hard Lefschetz theorem and a conjecture relating the pure part to absolutely indecomposable representations of a certain
Knot Invariants from FourDimensional Gauge Theory
 ADV.THEOR.MATH.PHYS
, 2011
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