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70
Membranes at Quantum Criticality
, 2009
"... We propose a quantum theory of membranes designed such that the groundstate wavefunction of the membrane with compact spatial topology Σh reproduces the partition function of the bosonic string on worldsheet Σh. The construction involves worldvolume matter at quantum criticality, described in the ..."
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Cited by 106 (0 self)
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We propose a quantum theory of membranes designed such that the groundstate wavefunction of the membrane with compact spatial topology Σh reproduces the partition function of the bosonic string on worldsheet Σh. The construction involves worldvolume matter at quantum criticality, described in the simplest case by Lifshitz scalars with dynamical critical exponent z = 2. This matter system must be coupled to a novel theory of worldvolume gravity, also exhibiting quantum criticality with z = 2. We first construct such a nonrelativistic “gravity at a Lifshitz point ” with z = 2 in D + 1 spacetime dimensions, and then specialize to the critical case of D = 2 suitable for the membrane worldvolume. We also show that in the secondquantized framework, the string partition function is reproduced if the spacetime ground state takes the form of a BoseEinstein condensate of membranes in
The effective action of type IIA CalabiYau orientifolds
"... The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau ..."
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Cited by 95 (6 self)
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The N = 1 effective action for generic type IIA CalabiYau orientifolds in the presence of background fluxes is computed from a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau orientifold and the background fluxes. The moduli space is found to be a Kähler subspace of the N = 2 moduli space and shown to coincide with the moduli space arising in compactification of Mtheory on a specific class of G2 manifolds. The superpotential depends on all geometrical moduli and vanishes at leading order when background fluxes are turned off. The N = 1 chiral coordinates linearize the appropriate instanton actions such that instanton effects can lead to holomorphic corrections of the superpotential. Mirror symmetry between type IIA and type IIB orientifolds is shown to hold at the level of the effective action in the large volume – large complex structure limit.
Instanton counting, Macdonald function and the moduli space
 of Dbranes,” JHEP 0505 (2005) 039, arXiv:hepth/0502061
"... We argue the connection of Nekrasov’s partition function in the Ω background and the moduli space of Dbranes, suggested by the idea of geometric engineering and GopakumarVafa invariants. In the instanton expansion of N = 2 SU(2) YangMills theory the Nakrasov’s partition function with equivariant ..."
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Cited by 40 (5 self)
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We argue the connection of Nekrasov’s partition function in the Ω background and the moduli space of Dbranes, suggested by the idea of geometric engineering and GopakumarVafa invariants. In the instanton expansion of N = 2 SU(2) YangMills theory the Nakrasov’s partition function with equivariant parameters ǫ1,ǫ2 of toric action on C 2 factorizes correctly as the character of SU(2)L ×SU(2)R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2branes on (local) F0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T 2 action allows us to obtain the generating functions of equivariant χy and elliptic Gravity/gauge theory correspondence is one of important subjects in the recent developments of nonperturbative string theory and Dbranes are the crucial dynamical objects for understanding the correspondence. In topological theory the correspondence
Two Dimensional KodairaSpencer Theory and Three Dimensional ChernSimons Gravity, arXiv:0711.1932 [hepth
"... Motivated by the sixdimensional formulation of KodairaSpencer theory for CalabiYau threefolds, we formulate a twodimensional version and argue that this is the relevant field theory for the target space of local topological Bmodel with a geometry based on a Riemann surface. We show that the War ..."
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Cited by 26 (4 self)
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Motivated by the sixdimensional formulation of KodairaSpencer theory for CalabiYau threefolds, we formulate a twodimensional version and argue that this is the relevant field theory for the target space of local topological Bmodel with a geometry based on a Riemann surface. We show that the Ward identities of this quantum theory is equivalent to recursion relations recently proposed by Eynard and Orantin to solve the topological B model. Our derivation provides a conceptual explanation of this link and reveals a hidden affine SL2 symmetry. Moreover we argue that our results provide the strongest evidence yet of the existence of topological M theory in one higher dimension, which in this case can be closely related to SL2 ChernSimons formulation of three dimensional gravity. November
Loop quantum gravity: An outside view
, 2005
"... We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the offshell (‘strong’) closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of th ..."
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Cited by 24 (0 self)
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We review aspects of loop quantum gravity in a pedagogical manner, with the aim of enabling a precise but critical assessment of its achievements so far. We emphasise that the offshell (‘strong’) closure of the constraint algebra is a crucial test of quantum spacetime covariance, and thereby of the consistency, of the theory. Special attention is paid to the appearance of a large number of ambiguities, in particular in the formulation of the Hamiltonian constraint. Developing suitable approximation methods to establish a connection with classical gravity on the one hand, and with the physics of elementary particles on the other, remains a major challenge. Contents 1 Key questions 2
The effective action of type II CalabiYau orientifolds,” Fortsch
 Phys
"... This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB CalabiYau orientifolds in the presence of background fluxes by using a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determi ..."
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Cited by 21 (3 self)
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This article first reviews the calculation of the N = 1 effective action for generic type IIA and type IIB CalabiYau orientifolds in the presence of background fluxes by using a KaluzaKlein reduction. The Kähler potential, the gauge kinetic functions and the fluxinduced superpotential are determined in terms of geometrical data of the CalabiYau orientifold and the background fluxes. As a new result, it is shown that the chiral description directly relates to Hitchin’s generalized geometry encoded by special odd and even forms on a threefold, whereas a dual formulation with several linear multiplets makes contact to the underlying N = 2 special geometry. In type IIB setups, the fluxpotentials can be expressed in terms of superpotentials, Dterms and, generically, a massive linear multiplet. The type IIA superpotential depends on all geometric moduli of the theory. It is reviewed, how type IIA orientifolds arise as a special limit of Mtheory compactified on specific G2 manifolds by matching the effective actions. In a similar spirit type IIB orientifolds are shown to descend from Ftheory on a specific class of CalabiYau fourfolds. In addition, mirror symmetry for CalabiYau orientifolds is briefly discussed and it is shown that the N = 1 chiral coordinates linearize the appropriate instanton actions.
Nonsupersymmetric Black Holes and Topological Strings
, 2007
"... We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one pa ..."
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Cited by 18 (1 self)
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We study nonsupersymmetric, extremal 4 dimensional black holes which arise upon compactification of type II superstrings on CalabiYau threefolds. We propose a generalization of the OSV conjecture for higher derivative corrections to the nonsupersymmetric black hole entropy, in terms of the one parameter refinement of topological string introduced by Nekrasov. We also study the attractor mechanism for nonsupersymmetric black holes and show how the inverse problem of fixing charges in terms of the attractor value of CY moduli can be explicitly solved.
Massless and massive three dimensional super Yang–Mills theory and mini–twistor string theory
 REV. D
, 2005
"... We propose various ways of adding mass terms to threedimensional twistor string theory. We begin with a review of minitwistor space—the reduction of D = 4 twistor space to D = 3. We adapt the two proposals for twistor string theory, Witten’s and Berkovits’s, to D = 3 super YangMills theory. In Be ..."
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Cited by 17 (1 self)
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We propose various ways of adding mass terms to threedimensional twistor string theory. We begin with a review of minitwistor space—the reduction of D = 4 twistor space to D = 3. We adapt the two proposals for twistor string theory, Witten’s and Berkovits’s, to D = 3 super YangMills theory. In Berkovits’s model, we identify the enhanced Rsymmetry. We then construct Bmodel topological string theories that, we propose, correspond to D = 3 YangMills theory with massive spinors and massive and massless scalars in the adjoint representation of the gauge group. We also analyze the counterparts of these constructions in Berkovits’s model. Some of our constructions can be lifted to D = 4, where infinitesimal mass terms correspond to VEVs of certain superconformal gravity fields.