arXiv subjects

Amir-Kian Kashani-Poor

Publications and source records attributed to Amir-Kian Kashani-Poor.

35 records · Page 2Linked to original sources

arXiv2013

Enhanced supersymmetry from vanishing Euler number

We argue that compactifications on Calabi-Yau threefolds with vanishing Euler number yield effective four dimensional theories exhibiting (spontaneously broken) N=4 supersymmetry. To this end, we derive the low-energy effective action for general SU(2) structure manifolds in type IIA string theory and show its consistency with gauged N=4 supergravity. Focusing on the special case of Calabi-Yau manifolds with vanishing Euler number, we explain the absence of perturbative corrections at the two-derivative level. In addition, we conjecture that all non-perturbative corrections are governed and constrained by the couplings of N=4 massive gravitino multiplets.

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arXiv2010

A matrix model for the topological string II: The spectral curve and mirror geometry

In a previous paper, we presented a matrix model reproducing the topological string partition function on an arbitrary given toric Calabi-Yau manifold. Here, we study the spectral curve of our matrix model and thus derive, upon imposing certain minimality assumptions on the spectral curve, the large volume limit of the BKMP "remodeling the B-model" conjecture, the claim that Gromov-Witten invariants of any toric Calabi-Yau 3-fold coincide with the spectral invariants of its mirror curve.

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arXiv2010

A matrix model for the topological string I: Deriving the matrix model

We construct a matrix model that reproduces the topological string partition function on arbitrary toric Calabi-Yau 3-folds. This demonstrates, in accord with the BKMP "remodeling the B-model" conjecture, that Gromov-Witten invariants of any toric Calabi-Yau 3-fold can be computed in terms of the spectral invariants of a spectral curve. Moreover, it proves that the generating function of Gromov-Witten invariants is a tau function for an integrable hierarchy. In a follow-up paper, we will explicitly construct the spectral curve of our matrix model and argue that it equals the mirror curve of the toric Calabi-Yau manifold.

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arXiv2009

Crystal melting on toric surfaces

We study the relationship between the statistical mechanics of crystal melting and instanton counting in N=4 supersymmetric U(1) gauge theory on toric surfaces. We argue that, in contrast to their six-dimensional cousins, the two problems are related but not identical. We develop a vertex formalism for the crystal partition function, which calculates a generating function for the dimension 0 and 1 subschemes of the toric surface, and describe the modifications required to obtain the corresponding gauge theory partition function.

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arXiv2009

Exploiting N=2 in consistent coset reductions of type IIA

We study compactifications of type IIA supergravity on cosets exhibiting SU(3) structure. We establish the consistency of the truncation based on left-invariance, providing a justification for the choice of expansion forms which yields gauged N=2 supergravity in 4 dimensions. We explore N=1 solutions of these theories, emphasizing the requirements of flux quantization, as well as their non-supersymmetric companions. In particular, we obtain a no-go result for de Sitter solutions at string tree level, and, exploiting the enhanced leverage of the N=2 setup, provide a preliminary analysis of the existence of de Sitter vacua at all string loop order.

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arXiv2008

Phase space polarization and the topological string: a case study

We review and elaborate on our discussion in hep-th/0606112 on the interplay between the target space and the worldsheet description of the open topological string partition function, for the example of the conifold. We discuss the appropriate phase space and canonical form for the system. We find a map between choices of polarization and the worldsheet description, based on which we study the behavior of the partition function under canonical transformations.

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arXiv2007

Nearly Kaehler Reduction

We consider compactification of type IIA supergravity on nearly Kaehler manifolds. These represent a simple class of SU(3) structure manifolds which includes S^6 and CP^3. We exhibit for the first time an explicit reduction ansatz in this context, obtaining an N=2 gauged supergravity in 4d with a single vector and hypermultiplet. We verify that supersymmetric solutions of the 4d theory lift to 10d solutions. Along the way, we discuss questions related to encountering both electric and magnetic charges in the 4d theory.

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arXiv2007

Towards reduction of type II theories on SU(3) structure manifolds

We revisit the reduction of type II supergravity on SU(3) structure manifolds, conjectured to lead to gauged N=2 supergravity in 4 dimensions. The reduction proceeds by expanding the invariant 2- and 3-forms of the SU(3) structure as well as the gauge potentials of the type II theory in the same set of forms, the analogues of harmonic forms in the case of Calabi-Yau reductions. By focussing on the metric sector, we arrive at a list of constraints these expansion forms should satisfy to yield a base point independent reduction. Identifying these constraints is a first step towards a first-principles reduction of type II on SU(3) structure manifolds.

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arXiv2007

The Wave Function Behavior of the Open Topological String Partition Function on the Conifold

We calculate the topological string partition function to all genus on the conifold, in the presence of branes. We demonstrate that the partition functions for different brane backgrounds (smoothly connected along a quantum corrected moduli space) can be interpreted as the same wave function in different polarizations. This behavior has a natural interpretation in the Chern-Simons target space description of the topological theory. Our detailed analysis however indicates that non-perturbatively, a modification of real Chern-Simons theory is required to capture the correct target space theory of the topological string. We perform our calculations in the framework of a free fermion representation of the open topological string, demonstrating that this framework extends beyond the simple C^3 geometry. The notion of a fermionic brane creation operator arises in this setting, and we study to what extent the wave function properties of the partition function can be extended to this operator.

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arXiv2006

The Vertex on a Strip

We demonstrate that for a broad class of local Calabi-Yau geometries built around a string of IP^1's - those whose toric diagrams are given by triangulations of a strip - we can derive simple rules, based on the topological vertex, for obtaining expressions for the topological string partition function in which the sums over Young tableaux have been performed. By allowing non-trivial tableaux on the external legs of the corresponding web diagrams, these strips can be used as building blocks for more general geometries. As applications of our result, we study the behavior of topological string amplitudes under flops, as well as check Nekrasov's conjecture in its most general form.

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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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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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arXiv2004

Moduli Potentials in Type IIA Compactifications with RR and NS Flux

We describe a simple class of type IIA string compactifications on Calabi-Yau manifolds where background fluxes generate a potential for the complex structure moduli, the dilaton, and the Kähler moduli. This class of models corresponds to gauged N=2 supergravities, and the potential is completely determined by a choice of gauging and by data of the N=2 Calabi-Yau model - the prepotential for vector multiplets and the quaternionic metric on the hypermultiplet moduli space. Using mirror symmetry, one can determine many (though not all) of the quantum corrections which are relevant in these models.

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arXiv2004

Instanton Counting and Chern-Simons Theory

The instanton partition function of N=2, D=4 SU(2) gauge theory is obtained by taking the field theory limit of the topological open string partition function, given by a Chern-Simons theory, of a CY3-fold. The CY3-fold on the open string side is obtained by geometric transition from local F_0 which is used in the geometric engineering of the SU(2) theory. The partition function obtained from the Chern-Simons theory agrees with the closed topological string partition function of local F_0 proposed recently by Nekrasov. We also obtain the partition functions for local F_1 and F_2 CY3-folds and show that the topological string amplitudes of all local Hirzebruch surfaces give rise to the same field theory limit. It is shown that a generalization of the topological closed string partition function whose field theory limit is the generalization of the instanton partition function, proposed by Nekrasov, can be determined easily from the Chern-Simons theory.

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arXiv2003

SU(N) Geometries and Topological String Amplitudes

It has been conjectured recently that the field theory limit of the topological string partition functions, including all higher genus contributions, for the family of CY3-folds giving rise to N=2 4D SU(N) gauge theory via geometric engineering can be obtained from gauge instanton calculus. We verify this surprising conjecture by calculating the partition functions for such local CYs using diagrammatic techniques inspired by geometric transitions. Determining the Gopakumar-Vafa invariants for these geometries to all orders in the fiber wrappings allows us to take the field theory limit.

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arXiv2001

Discrete Symmetries of the Superpotential and Calculation of Disk Invariants

The integrality of Ooguri-Vafa disk invariants is verified using discrete symmetries of the superpotential of the mirror Landau-Ginzburg theory to calculate quantum corrections to the boundary variables. We show that these quantum corrections are completely determined if we assume that the discrete symmetry of the superpotential also holds in terms of the quantum corrected variables. We discuss the case of local P^2 blown up at three points and local F_2 blown up at two points in detail.

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