Results 1  10
of
131
The topological vertex
, 2003
"... We construct a cubic field theory which provides all genus amplitudes of the topological Amodel for all noncompact toric CalabiYau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed CalabiYau, with Schwinger parameters playing the role of Kähler classes of the th ..."
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Cited by 167 (25 self)
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We construct a cubic field theory which provides all genus amplitudes of the topological Amodel for all noncompact toric CalabiYau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed CalabiYau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the Bmodel mirror which is the quantum KodairaSpencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the Bbranes on the mirror Riemann
Black holes, qdeformed 2d YangMills, and nonperturbative topological strings
, 2004
"... We count the number of bound states of BPS black holes on local CalabiYau threefolds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a qdeformed YangMills 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 CalabiYau threefolds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a qdeformed YangMills 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 Dbrane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The subleading chiral blocks involve topological string amplitudes with Dbrane insertions at (2g − 2) points on the Riemann surface analogous to the Ω points in the large N 2d YangMills theory. The finite N amplitude provides a nonperturbative definition of topological strings in these backgrounds. This also leads to a novel nonperturbative formulation of c = 1 noncritical string at the selfdual radius.
Topological strings and (almost) modular forms
, 2007
"... The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the cho ..."
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Cited by 93 (10 self)
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The Bmodel topological string theory on a CalabiYau threefold X has a symmetry group Γ, generated by monodromies of the periods of X. This acts on the topological string wave function in a natural way, governed by the quantum mechanics of the phase space H 3 (X). We show that, depending on the choice of polarization, the genus g topological string amplitude is either a holomorphic quasimodular form or an almost holomorphic modular form of weight 0 under Γ. Moreover, at each genus, certain combinations of genus g amplitudes are both modular and holomorphic. We illustrate this for the local CalabiYau manifolds giving rise to SeibergWitten gauge theories in four dimensions and local IP2 and IP1×IP1. As a byproduct, we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space, which we use to give predictions for GromovWitten invariants of the orbifold C 3 / Z3.
Topological string amplitudes, complete intersection Calabi–Yau spaces and threshold corrections
, 2005
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Lectures on localization and matrix models in Supersymmetric Chern–simons–matter Theories
, 2012
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MultiMatrix Models and TriSasaki Einstein Spaces
, 2010
"... Localization methods reduce the path integrals in N ≥ 2 supersymmetric ChernSimons gauge theories on S 3 to multimatrix integrals. A recent evaluation of such a twomatrix integral for the N = 6 superconformal U(N) × U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, ex ..."
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Cited by 46 (2 self)
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Localization methods reduce the path integrals in N ≥ 2 supersymmetric ChernSimons gauge theories on S 3 to multimatrix integrals. A recent evaluation of such a twomatrix integral for the N = 6 superconformal U(N) × U(N) ABJM theory produced detailed agreement with the AdS/CFT correspondence, explaining in particular the N 3/2 scaling of the free energy. We study a class of pmatrix integrals describing N = 3 superconformal U(N) p ChernSimons gauge theories. We present a simple method that allows us to evaluate the eigenvalue densities and the free energies in the large N limit keeping the ChernSimons levels ki fixed. The dual Mtheory backgrounds are AdS4×Y, where Y are sevendimensional triSasaki Einstein spaces specified by the ki. The gravitational free energy scales inversely with the square root of the volume of Y. We find a general formula for the pmatrix free energies that agrees with the available results for volumes of the triSasaki Einstein spaces Y, thus providing a thorough test of the corresponding AdS4/CFT3 dualities. This formula is consistent with the Seiberg duality conjectured for ChernSimons gauge theories.
Soft matrix models and ChernSimons partition functions,” Mod
 Phys. Lett. A
, 2004
"... Abstract. We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. Relying on simple considerations from the moment problem and orthogonal polynomials, we show general features ..."
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Cited by 41 (14 self)
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Abstract. We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. Relying on simple considerations from the moment problem and orthogonal polynomials, we show general features of their density of states, correlation functions and loop averages. Some examples are worked out in detail. In addition, some of these models are equivalent, by a simple mapping, to matrix models that have appeared recently in connection with ChernSimons theory. The models can be solved with q deformed orthogonal polynomials (StieltjesWigert polynomials), and the deformation parameter turns out to be the usual q parameter in ChernSimons theory. In this way, we give a matrix model computation of the ChernSimons partition function on S 3 and show that there are an infinite number of matrix models with this partition function. 1.