arXiv subjects

C. I. Lazaroiu

Publications and source records attributed to C. I. Lazaroiu.

At least 37 records · Page 2Linked to original sources

arXiv2004

Superpotentials, A-infinity Relations and WDVV Equations for Open Topological Strings

We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A-infinity relations (which generalize associativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss integrability of amplitudes with respect to bulk and boundary deformations, and write down the analogs of WDVV equations for the space-time superpotential. We also study the structure of these equations from a string field theory point of view. As an application, we determine the effective superpotential for certain families of D-branes in B-twisted topological minimal models, as a function of both closed and open string moduli. This provides an exact description of tachyon condensation in such models, which allows one to determine the truncation of the open string spectrum in a simple manner.

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arXiv2004

Puzzles for Matrix Models of Chiral Field Theories

We summarize the field-theory/matrix model correspondence for a chiral N=1 model with matter in the adjoint, antisymmetric and conjugate symmetric representations as well as eight fundamentals to cancel the chiral anomaly. The associated holomorphic matrix model is consistent only for two fundamental fields, which requires a modification of the original Dijkgraaf-Vafa conjecture. The modified correspondence holds in spite of this mismatch.

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arXiv2004

Localization and traces in open-closed topological Landau-Ginzburg models

We reconsider the issue of localization in open-closed B-twisted Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful analsysis of zero-mode reduction, we show that the closed model allows for a one-parameter family of localization pictures, which generalize the standard residue representation. The parameter $λ$ which indexes these pictures measures the area of worldsheets with $S^2$ topology, with the residue representation obtained in the limit of small area. In the boundary sector, we find a double family of such pictures, depending on parameters $λ$ and $μ$ which measure the area and boundary length of worldsheets with disk topology. We show that setting $μ=0$ and varying $λ$ interpolates between the localization picture of the B-model with a noncompact target space and a certain residue representation proposed recently. This gives a complete derivation of the boundary residue formula, starting from the explicit construction of the boundary coupling. We also show that the various localization pictures are related by a semigroup of homotopy equivalences.

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arXiv2003

On the structure of open-closed topological field theory in two dimensions

I discuss the general formalism of two-dimensional topological field theories defined on open-closed oriented Riemann surfaces, starting from an extension of Segal's geometric axioms. Exploiting the topological sewing constraints allows for the identification of the algebraic structure governing such systems. I give a careful treatment of bulk-boundary and boundary-bulk correspondences, which are responsible for the relation between the closed and open sectors. The fact that these correspondences need not be injective nor surjective has interesting implications for the problem of classifying `boundary conditions'. In particular, I give a clear geometric derivation of the (topological) boundary state formalism and point out some of its limitations. Finally, I formulate the problem of classifying (on-shell) boundary extensions of a given closed topological field theory in purely algebraic terms and discuss their reducibility.

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arXiv2003

On the boundary coupling of topological Landau-Ginzburg models

I propose a general form for the boundary coupling of B-type topological Landau-Ginzburg models. In particular, I show that the relevant background in the open string sector is a (generally non-Abelian) superconnection of type (0,1) living in a complex superbundle defined on the target space, which I allow to be a non-compact Calabi-Yau manifold. This extends and clarifies previous proposals. Generalizing an argument due to Witten, I show that BRST invariance of the partition function on the worldsheet amounts to the condition that the (0,<= 2) part of the superconnection's curvature equals a constant endomorphism plus the Landau-Ginzburg potential times the identity section of the underlying superbundle. This provides the target space equations of motion for the open topological model.

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arXiv2003

Chiral field theories from conifolds

We discuss the geometric engineering and large n transition for an N=1 U(n) chiral gauge theory with one adjoint, one conjugate symmetric, one antisymmetric and eight fundamental chiral multiplets. Our IIB realization involves an orientifold of a non-compact Calabi-Yau A_2 fibration, together with D5-branes wrapping the exceptional curves of its resolution as well as the orientifold fixed locus. We give a detailed discussion of this background and of its relation to the Hanany-Witten realization of the same theory. In particular, we argue that the T-duality relating the two constructions maps the Z_2 orientifold of the Hanany-Witten realization into a Z_4 orientifold in type IIB. We also discuss the related engineering of theories with SO/Sp gauge groups and symmetric or antisymmetric matter.

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arXiv2003

On Sp(0) factors and orientifolds

We discuss the geometric engineering of SO/Sp gauge theories with symmetric or antisymmetric tensor matter and show that the `mysterious' rank zero gauge group factors observed by a few authors can be traced back to the effects of an orientifold which survives the geometric transition. By mapping the Konishi constraints of such models to those of the U(N) theory with adjoint matter, we show that the required shifts in the ranks of the unbroken gauge group components is due to the flux contribution of the orientifold after the transition.

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arXiv2003

Chiral field theories, Konishi anomalies and matrix models

We study a chiral N=1, U(N) field theory in the context of the Dijkgraaf-Vafa correspondence. Our model contains one adjoint, one conjugate symmetric and one antisymmetric chiral multiplet, as well as eight fundamentals. We compute the generalized Konishi anomalies and compare the chiral ring relations they induce with the loop equations of the (intrinsically holomorphic) matrix model defined by the tree-level superpotential of the field theory. Surprisingly, we find that the matrix model is well-defined only if the number of flavors equals two! Despite this mismatch, we show that the 1/N expansion of the loop equations agrees with the generalized Konishi constraints. This indicates that the matrix model - gauge theory correspondence should generally be modified when applied to theories with net chirality. We also show that this chiral theory produces the same gaugino superpotential as a nonchiral SO(N) model with a single symmetric multiplet and a polynomial superpotential.

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arXiv2003

(Anti)symmetric matter and superpotentials from IIB orientifolds

We study the IIB engineering of N=1 gauge theories with unitary gauge group and matter in the adjoint and (anti)symmetric representations. We show that such theories can be obtained as Z2 orientifolds of Calabi-Yau A2 fibrations, and discuss the explicit T-duality transformation to an orientifolded Hanany-Witten construction. The low energy dynamics is described by a geometric transition of the orientifolded background. Unlike previously studied cases, we show that the orientifold 5-`plane' survives the transition, thus bringing a nontrivial contribution to the effective superpotential. We extract this contribution by using matrix model results and compare with geometric data. A Higgs branch of our models recovers the engineering of SO/Sp theories with adjoint matter through an O5-`plane' T-dual to an O6-plane. We show that the superpotential agrees with that produced by engineering through an O5-`plane' dual to an O4-plane, even though the orientifold of this second construction is replaced by fluxes after the transition.

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arXiv2003

D-brane categories

This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic perspective, and with a focus on applications to homological mirror symmetry.

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arXiv2003

Holomorphic matrix models

This is a study of holomorphic matrix models, the matrix models which underlie the conjecture of Dijkgraaf and Vafa. I first give a systematic description of the holomorphic one-matrix model. After discussing its convergence sectors, I show that certain puzzles related to its perturbative expansion admit a simple resolution in the holomorphic set-up. Constructing a `complex' microcanonical ensemble, I check that the basic requirements of the conjecture (in particular, the special geometry relations involving chemical potentials) hold in the absence of the hermicity constraint. I also show that planar solutions of the holomorphic model probe the entire moduli space of the associated algebraic curve. Finally, I give a brief discussion of holomorphic $ADE$ models, focusing on the example of the $A_2$ quiver, for which I extract explicitly the relevant Riemann surface. In this case, use of the holomorphic model is crucial, since the Hermitian approach and its attending regularization would lead to a singular algebraic curve, thus contradicting the requirements of the conjecture. In particular, I show how an appropriate regularization of the holomorphic $A_2$ model produces the desired smooth Riemann surface in the limit when the regulator is removed, and that this limit can be described as a statistical ensemble of `reduced' holomorphic models.

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arXiv2003

Geometric regularizations and dual conifold transitions

We consider a geometric regularization for the class of conifold transitions relating D-brane systems on noncompact Calabi-Yau spaces to certain flux backgrounds. This regularization respects the SL(2,Z) invariance of the flux superpotential, and allows for computation of the relevant periods through the method of Picard-Fuchs equations. The regularized geometry is a noncompact Calabi-Yau which can be viewed as a monodromic fibration, with the nontrivial monodromy being induced by the regulator. It reduces to the original, non-monodromic background when the regulator is removed. Using this regularization, we discuss the simple case of the local conifold, and show how the relevant field-theoretic information can be extracted in this approach.

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arXiv2003

Constructing Gauge Theory Geometries from Matrix Models

We use the matrix model -- gauge theory correspondence of Dijkgraaf and Vafa in order to construct the geometry encoding the exact gaugino condensate superpotential for the N=1 U(N) gauge theory with adjoint and symmetric or anti-symmetric matter, broken by a tree level superpotential to a product subgroup involving U(N_i) and SO(N_i) or Sp(N_i/2) factors. The relevant geometry is encoded by a non-hyperelliptic Riemann surface, which we extract from the exact loop equations. We also show that O(1/N) corrections can be extracted from a logarithmic deformation of this surface. The loop equations contain explicitly subleading terms of order 1/N, which encode information of string theory on an orientifolded local quiver geometry.

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arXiv2002

Domain walls of N=2 supergravity in five dimensions from hypermultiplet moduli spaces

We study domain wall solutions in d=5, N=2 supergravity coupled to a single hypermultiplet whose moduli space is described by certain inhomogeneous, toric ESD manifolds constructed recently by Calderbank and Singer. Upon gauging a generic U(1) isometry of these spaces, we obtain an infinite family of models whose "superpotential" admits an arbitrary number of isolated critical points. By investigating the associated supersymmetric flows, we prove the existence of domain walls of Randall-Sundrum type for each member of our family, and find chains of domain walls interpolating between various AdS_5 backgrounds. Our models are described by a discrete infinity of smooth and complete one-hypermultiplet moduli spaces, which live on an open subset of the minimal resolution of certain cyclic quotient singularities. These spaces generalize the Pedersen metrics considered recently by Behrndt and Dall' Agata.

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arXiv2002

An analytic torsion for graded D-branes

I consider the semiclassical approximation of the graded Chern-Simons field theories describing certain systems of topological A type branes in the large radius limit of Calabi-Yau compactifications. I show that the semiclassical partition function can be expressed in terms of a certain (differential) numerical invariant which is a version of the analytic torsion of Ray and Singer, but associated with flat graded superbundles. I also discuss a `twisted' version of the Ray-Singer norm, and show its independence of metric data. As illustration, I consider graded D-brane pairs of unit relative grade with a scalar condensate in the boundary condition changing sector. For the particularly simple case when the reference flat connections are trivial, I show that the generalized torsion reduces to a power of the classical Ray-Singer invariant of the base 3-manifold.

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arXiv2002

Enhanced gauge symmetry from `toric' G_2 cones

We review our recent work on M-theory compactifications on `toric' G_2 cones, a class of models which generalize those recently considered by Acharya and Witten and lead to chiral matter in four dimensions. We explain our criteria for identifying the gauge group content of such theories and briefly discuss the associated metrics.

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arXiv2002

M-theory on `toric' G_2 cones and its type II reduction

We analyze a class of conical G_2 metrics admitting two commuting isometries, together with a certain one-parameter family of G_2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we write down the explicit G_2 metric for the most general member of this family and extract the IIA reduction of M-theory on such backgrounds, as well as its type IIB dual. By studying the asymptotics of type II fields around the relevant loci, we confirm the interpretation of such backgrounds in terms of localized IIA 6-branes and delocalized IIB 5-branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS forms in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.

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arXiv2002

M-theory compactifications on certain `toric' cones of $G_2$ holonomy

We develop methods to study the singularities of certain $G_2$ cones related to toric hyperkahler spaces and Einstein selfdual orbifolds. This allows us to determine the low energy gauge groups of chiral N=1 compactifications of M-theory on a large family of such backgrounds, which includes the models recently studied by Acharya and Witten. All M-theory compactifications belonging to our family admit a $T^2$ of isometries, and therefore T-dual IIA and IIB descriptions. We argue that reduction through such an isometry leads generically to systems of weakly and strongly coupled IIA 6-branes, T-dual to delocalized type IIB 5-branes. We find a simple criterion for the existence of a `good' isometry which leads to IIA models containing only weakly-coupled D6-branes, and construct examples of such backgrounds. Some of the methods we develop may also apply to different situations, such as the study of certain singularities in the hypermultiplet moduli space of N=2 supergravity in four dimensions.

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