arXiv subjects

Alessandro Tomasiello

Publications and source records attributed to Alessandro Tomasiello.

90 records · Page 5Linked to original sources

arXiv2006

An index for the Dirac operator on D3 branes with background fluxes

We study the problem of instanton generated superpotentials in Calabi-Yau orientifold compactifications directly in type IIB string theory. To this end, we derive the Dirac equation on a Euclidean D3 brane in the presence of background fluxes. We propose an index which governs whether the generation of a superpotential in the effective 4d theory by D3 brane instantons is possible. Applying the formalism to various classes of examples, including the K3 x T^2/Z_2 orientifold, in the absence and presence of fluxes, we show that our results are consistent with conclusions attainable via duality from an M-theory analysis.

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arXiv2006

Black Hole Attractors and Pure Spinors

We construct black hole attractor solutions for a wide class of N=2 compactifications. The analysis is carried out in ten dimensions and makes crucial use of pure spinor techniques. This formalism can accommodate non-Kaehler manifolds as well as compactifications with flux, in addition to the usual Calabi-Yau case. At the attractor point, the charges fix the moduli according to sum_k f_k = Im(C Phi), where Phi is a pure spinor of odd (even) chirality in IIB (A). For IIB on a Calabi-Yau, Phi=Omega and the equation reduces to the usual one. Methods in generalized complex geometry can be used to study solutions to the attractor equation.

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arXiv2005

Complex/Symplectic Mirrors

We construct a class of symplectic non--Kaehler and complex non--Kaehler string theory vacua, extending and providing evidence for an earlier suggestion by Polchinski and Strominger. The class admits a mirror pairing by construction. Comparing hints from a variety of sources, including ten--dimensional supergravity and KK reduction on SU(3)--structure manifolds, suggests a picture in which string theory extends Reid's fantasy to connect classes of both complex non-Kaehler and symplectic non-Kaehler manifolds.

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arXiv2005

Counting fermionic zero modes on M5 with fluxes

We study the Dirac equation on an M5 brane wrapped on a divisor in a Calabi--Yau fourfold in the presence of background flux. We reduce the computation of the normal bundle U(1) anomaly to counting the solutions of a finite--dimensional linear system on cohomology. This system depends on the choice of flux. In an example, we find that the presence of flux changes the anomaly and allows instanton corrections to the superpotential which would otherwise be absent.

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arXiv2005

A Stringy Test of Flux-Induced Isometry Gauging

Supergravity analysis suggests that the effect of fluxes in string theory compactifications is to gauge isometries of the scalar manifold. However, isometries are generically broken by brane instanton effects. Here we demonstrate how fluxes protect exactly those isometries from quantum corrections which are gauged according to the classical supergravity analysis. We also argue that all other isometries are generically broken.

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arXiv2005

Topological mirror symmetry with fluxes

Motivated by SU(3) structure compactifications, we show explicitly how to construct half--flat topological mirrors to Calabi--Yau manifolds with NS fluxes. Units of flux are exchanged with torsion factors in the cohomology of the mirror; this is the topological complement of previous differential--geometric mirror rules. The construction modifies explicit SYZ fibrations for compact Calabi--Yaus. The results are of independent interest for SU(3) compactifications. For example one can exhibit explicitly which massive forms should be used for Kaluza--Klein reduction, proving previous conjectures. Formality shows that these forms carry no topological information; this is also confirmed by infrared limits and old classification theorems.

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arXiv2004

Generalized complex manifolds and supersymmetry

We find a worldsheet realization of generalized complex geometry, a notion introduced recently by Hitchin which interpolates between complex and symplectic manifolds. The two-dimensional model we construct is a supersymmetric relative of the Poisson sigma model used in context of deformation quantization.

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arXiv2004

Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds

We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form exp(iJ) and the holomorphic form Omega. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: exp(iJ) is closed under the action of the twisted exterior derivative in IIA theory, and similarly Omega is closed in IIB. Modulo a different action of the B-field, this means that supersymmetric SU(3)-structure manifolds are all generalized Calabi-Yau manifolds, as defined by Hitchin. An equivalent, and somewhat more conventional, description is given as a set of relations between the components of intrinsic torsions modified by the NS flux and the Clifford products of RR fluxes with pure spinors, allowing for a classification of type II supersymmetric vacua on six-manifolds. We find in particular that supersymmetric six-manifolds are always complex for IIB backgrounds while they are twisted symplectic for IIA.

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arXiv2004

Type II Strings and Generalized Calabi-Yau Manifolds

This is a short version of hep-th/0406137. We show that the supersymmetry transformations for type II string theories on six-manifolds can be written as differential conditions on a pair of pure spinors, the exponentiated Kahler form e^{iJ} and the holomorphic form Omega. The equations are explicitly symmetric under exchange of the two pure spinors and a choice of even or odd-rank RR field. This is mirror symmetry for manifolds with torsion. Moreover, RR fluxes affect only one of the two equations: e^{iJ} is closed under the action of the twisted exterior derivative in IIA theory, and similarly Omega is closed in IIB. This means that supersymmetric SU(3)-structure manifolds are always complex in IIB while they are twisted symplectic in IIA. Modulo a different action of the B-field, these are all generalized Calabi-Yau manifolds, as defined by Hitchin.

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arXiv2003

Mirror symmetric SU(3)-structure manifolds with NS fluxes

When string theory is compactified on a six-dimensional manifold with a nontrivial NS flux turned on, mirror symmetry exchanges the flux with a purely geometrical composite NS form associated with lack of integrability of the complex structure on the mirror side. Considering a general class of T^3-fibered geometries admitting SU(3) structure, we find an exchange of pure spinors (e^{iJ} and Ω) in dual geometries under fiberwise T-duality, and study the transformations of the NS flux and the components of intrinsic torsion. A complementary study of action of twisted covariant derivatives on invariant spinors allows to extend our results to generic geometries and formulate a proposal for mirror symmetry in compactifications with NS flux.

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arXiv2003

Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures

We consider Minkowski compactifications of M-theory on generic seven-dimensional manifolds. After analyzing the conditions on the four-form flux, we establish a set of relations between the components of the intrinsic torsion of the internal manifold and the components of the four-form flux needed for preserving supersymmetry. The existence of two nowhere vanishing vectors on any seven-manifold with G_2 structure plays a crucial role in our analysis, leading to the possibility of four-dimensional compactifications with N=1 and N=2 supersymmetry.

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arXiv2003

Nontrivial RR two-form field strength and SU(3)-structure

We discuss how in the presence of a nontrivial RR two-form field strength and nontrivial dilaton the conditions of preserving supersymmetry on six-dimensional manifolds lead to generalized monopole and Killing spinor equations. We show that the manifold is Kähler in the ten-dimensional string frame if F_0^{(1,1)}=0. We then determine explicitly the intrinsic torsion of the SU(3)-structure on six-manifolds that result via Kaluza-Klein reduction from seven-manifolds with G_2-structure of generic intrinsic torsion. Lastly we give explicitly the intrinsic torsion of the SU(3)-structure for an N=1 supersymmetric background in the presence of nontrivial RR two-form field strength and nontrivial dilaton.

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arXiv2002

Kaluza-Klein bundles and manifolds of exceptional holonomy

We show how in the presence of RR two-form field strength the conditions for preserving supersymmetry on six- and seven-dimensional manifolds lead to certain generalizations of monopole equations. For six dimensions the string frame metric is Kaehler with the complex structure that descends from the octonions if in addition we assume F^{(1,1)}=0. The susy generator is a gauge covariantly constant spinor. For seven dimensions the string frame metric is conformal to a G_2 metric if in addition we assume the field strength to obey a selfduality constraint. Solutions to these equations lift to geometries of G_2 and Spin(7) holonomy respectively.

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arXiv2002

Variations on stability

We explore the effects of non-abelian dynamics of D-branes on their stability and introduce Hitchin-like modifications to previously-known stability conditions. The relation to brane-antibrane systems is used in order to rewrite the equations in terms of superconnections and arrive at deformed vortex equations.

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arXiv2002

D-branes on Calabi-Yau Manifolds and Superpotentials

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.

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arXiv2001

A-infinity structure and superpotentials

A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.

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arXiv2001

D-branes on Calabi-Yau manifolds and helices

We investigate further on the correspondence between branes on a Calabi-Yau in the large volume limit and in the orbifold limit. We conjecture a new procedure which improves computationally the McKay correspondence and prove it in a non trivial example. We point out the relevance of helices and try to draw some general conclusions about Beilinson theorem and McKay correspondence.

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arXiv2000

3D superconformal theories from Sasakian seven-manifolds: new nontrivial evidences for AdS_4/CFT_3

In this paper we discuss candidate superconformal N=2 gauge theories that realize the AdS/CFT correspondence with M--theory compactified on the homogeneous Sasakian 7-manifolds M^7 that were classified long ago. In particular we focus on the two cases M^7=Q^{1,1,1} and M^7=M^{1,1,1}, for the latter the Kaluza Klein spectrum being completely known. We show how the toric description of M^7 suggests the gauge group and the supersingleton fields. The conformal dimensions of the latter can be independently calculated by comparison with the mass of baryonic operators that correspond to 5-branes wrapped on supersymmetric 5-cycles and are charged with respect to the Betti multiplets. The entire Kaluza Klein spectrum of short multiplets agrees with these dimensions. Furthermore, the metric cone over the Sasakian manifold is a conifold algebraically embedded in some C^p. The ring of chiral primary fields is defined as the coordinate ring of C^p modded by the ideal generated by the embedding equations; this ideal has a nice characterization by means of representation theory. The entire Kaluza Klein spectrum is explained in terms of these vanishing relations. We give the superfield interpretation of all short multiplets and we point out the existence of many long multiplets with rational protected dimensions, whose presence and pattern seem to be universal in all compactifications.

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