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SasakiEinstein manifolds and volume minimisation
, 2006
"... We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian ..."
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Cited by 112 (7 self)
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We study a variational problem whose critical point determines the Reeb vector field for a Sasaki–Einstein manifold. This extends our previous work on Sasakian geometry by lifting the condition that the manifolds are toric. We show that the Einstein–Hilbert action, restricted to a space of Sasakian metrics on a link L in a Calabi–Yau cone M, is the volume functional, which in fact is a function on the space of Reeb vector fields. We relate this function both to the Duistermaat– Heckman formula and also to a limit of a certain equivariant index on M that counts holomorphic functions. Both formulae may be evaluated by localisation. This leads to a general formula for the volume function in terms of topological fixed point data. As a result we prove that the volume of any Sasaki–Einstein manifold, relative to that of the round sphere, is always an algebraic number. In complex dimension n = 3 these results provide, via AdS/CFT, the geometric counterpart of a–maximisation in four dimensional superconformal field theories. We also show that our variational problem dynamically sets to zero the Futaki
NonCritical Pure Spinor Superstrings
, 2006
"... We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spi ..."
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Cited by 15 (3 self)
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We construct noncritical pure spinor superstrings in two, four and six dimensions. We find explicitly the map between the RNS variables and the pure spinor ones in the linear dilaton background. The RNS variables map onto a patch of the pure spinor space and the holomorphic top form on the pure spinor space is an essential ingredient of the mapping. A basic feature of the map is the requirement of doubling the superspace, which we analyze in detail. We study the structure of the noncritical pure spinor space, which is different from the tendimensional one, and its quantum anomalies. We compute the pure spinor lowest lying BRST cohomology and find an agreement with the RNS spectra. The analysis is generalized to curved backgrounds and we construct as an example the noncritical pure spinor type IIA superstring on AdS4 with RR 4form flux.
Partition Functions, Localization, and the Chiral de Rham complex
, 2007
"... We propose a localization formula for the chiral de Rham complex generalizing the wellknown localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the nonlinear βγ system as a gauge theory. For ab ..."
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Cited by 5 (1 self)
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We propose a localization formula for the chiral de Rham complex generalizing the wellknown localization procedure in topological theories. Our formula takes into account the contribution due to the massive modes. The key to achieve this is to view the nonlinear βγ system as a gauge theory. For abelian gauge groups we are in the realm of toric geometry. Including the bc system, the formula reproduces the known results for the elliptic genus of toric varieties. We compute the partition function of several models.
Pure Spinor Partition Function Using Pade Approximants
 JHEP 0807
"... In a recent paper, the partition function (character) of tendimensional pure spinor worldsheet variables was calculated explicitly up to the fifth masslevel. In this letter, we propose a novel application of Padé approximants as a tool for computing the character of pure spinors. We get results up ..."
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Cited by 5 (2 self)
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In a recent paper, the partition function (character) of tendimensional pure spinor worldsheet variables was calculated explicitly up to the fifth masslevel. In this letter, we propose a novel application of Padé approximants as a tool for computing the character of pure spinors. We get results up to the twelfth masslevel. This work is a first step towards
Integrability of Type II Superstrings on RamondRamond Backgrounds in Various Dimensions
, 2007
"... Abstract: We consider type II superstrings on AdS backgrounds with RamondRamond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: noncritical superstrings on AdS2d and critical superstrings on AdSp × S p × CY. We work both in the Gr ..."
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Cited by 2 (1 self)
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Abstract: We consider type II superstrings on AdS backgrounds with RamondRamond flux in various dimensions. We realize the backgrounds as supercosets and analyze explicitly two classes of models: noncritical superstrings on AdS2d and critical superstrings on AdSp × S p × CY. We work both in the Green–Schwarz and in the pure spinor formalisms. We construct a oneparameter family of flat currents (a Lax connection), leading to an infinite number of conserved nonlocal charges, which imply the classical integrability of both sigmamodels. In the pure spinor formulation, we use the BRST symmetry to prove the quantum integrability of the sigmamodel. We discuss how classical κsymmetry implies oneloop conformal invariance. We consider the addition of spacefilling Dbranes to the pure spinor formalism.
YFormalism and Curved β−γ Systems
, 2008
"... We adopt the Yformalism to study β − γ systems on hypersurfaces. We compute the operator product expansions of gaugeinvariant currents and we discuss some applications of the Yformalism to model on CalabiYau spaces. ..."
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We adopt the Yformalism to study β − γ systems on hypersurfaces. We compute the operator product expansions of gaugeinvariant currents and we discuss some applications of the Yformalism to model on CalabiYau spaces.