arXiv subjects

Sebastian Franco

Publications and source records attributed to Sebastian Franco.

At least 55 records · Page 3Linked to original sources

arXiv2012

Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories

We investigate infinite families of 3d N=2 superconformal Chern-Simons quivers with an arbitrarily large number of gauge groups arising on M2-branes over toric CY_4's. These theories have the same matter content and superpotential of those on D3-branes probing cones over L^{a,b,a} Sasaki-Einstein manifolds. For all these infinite families, we explicitly show the correspondence between the free energy F on S^3 and the volume of the 7-dimensional base of the associated CY_4, even before extremization. Our results add to those existing in the literature, providing further support for the correspondence. We develop a lifting algorithm, based on the Type IIB realization of these theories, that takes from CY_3's to CY_4's and we use it to efficiently generate the models studied in the paper. We also introduce a procedure, based on the mapping between extremal points in the toric diagram (GLSM fields) and chiral fields in the quiver, which systematically translates symmetries of the toric diagram into constraints of the trial R-charges of the quiver, beyond those arising from marginality of the superpotential. This method can be exploited for reducing the dimension of the space of trial R-charges over which the free energy is maximized. Finally, we show that in all the infinite families we consider F^2 can be expressed, even off-shell, as a quartic function in R-charges associated to certain 5-cycles. This suggests that a quartic formula on R-charges, analogous to a similar cubic function for the central charge a in 4d, exists for all toric toric CY_4's and we present some ideas regarding its general form.

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arXiv2012

Towards the Continuous Limit of Cluster Integrable Systems

We initiate the study of how to extend the correspondence between dimer models and (0+1)-dimensional cluster integrable systems to (1+1) and (2+1)-dimensional continuous integrable field theories, addressing various points that are necessary for achieving this goal. We first study how to glue and split two integrable systems, from the perspectives of the spectral curve, the resolution of the associated toric Calabi-Yau 3-folds and Higgsing in quiver theories on D3-brane probes. We identify a continuous parameter controlling the decoupling between the components and present two complementary methods for determining the dependence on this parameter of the dynamical variables of the integrable system. Interested in constructing systems with an infinite number of degrees of freedom, we study the combinatorics of integrable systems built up from a large number of elementary components, and introduce a toy model capturing important features expected to be present in a continuous reformulation of cluster integrable systems.

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arXiv2011

Colored BPS Pyramid Partition Functions, Quivers and Cluster Transformations

We investigate the connections between flavored quivers, dimer models, and BPS pyramids for generic toric Calabi-Yau threefolds from various perspectives. We introduce a purely field theoretic definition of both finite and infinite pyramids in terms of quivers with flavors. These pyramids are associated to the counting of BPS invariants for generic toric Calabi-Yau threefolds. We discuss how cluster transformations provide an efficient recursive method for computing pyramid partition functions and show that the recursion is equivalent to the multidimensional octahedron recurrence. Transitions between different pyramids are related to Seiberg dualities, and we offer complimentary characterizations of these transitions in terms of the motion of zonotopes and duality webs. Our methods apply to completely general geometries including those with vanishing 4-cycles, which are associated to chiral quivers, thus overcoming one of the main limitations in the existing literature. We illustrate our ideas with explicit results for the infinite family of L^{a,b,c} geometries, dP_2, pseudo-dP_2, and dP_3. The counting of pyramid partitions for dP_1 gives rise to the Somos-4 sequence, while dP_2 and pseudo-dP_2 generate the Somos-5 sequence. Our results for dP_3 reproduce and extend those previously obtained for this theory, which were originally obtained from dimer shuffling.

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arXiv2011

Dimer Models, Integrable Systems and Quantum Teichmuller Space

We introduce a correspondence between dimer models (and hence superconformal quivers) and the quantum Teichmuller space of the Riemann surfaces associated to them by mirror symmetry. Via the untwisting map, every brane tiling gives rise to a tiling of the Riemann surface with faces surrounding punctures. We explain how to obtain an ideal triangulation by dualizing this tiling. In order to do so, tiling nodes of valence greater than 3 (equivalently superpotential terms of order greater than 3 in the corresponding quiver gauge theories) must be decomposed by the introduction of 2-valent nodes. From a quiver gauge theory perspective, this operation corresponds to integrating-in massive fields. Fock coordinates in Teichmuller space are in one-to-one correspondence with chiral fields in the quiver. We present multiple explicit examples, including infinite families of theories, illustrating how the right number of Fock coordinates is generated by this procedure. Finally, we explain how Chekhov and Fock commutation relations between coordinates give rise to the commutators associated to dimer models by Goncharov and Kenyon in the context of quantum integrable systems. For generic dimer models (i.e. those containing nodes that are not 3-valent), this matching requires the introduction of a natural generalization of Chekhov and Fock rules. We also explain how urban renewal in the original brane tiling (Seiberg duality for the quivers) is mapped to flips of the ideal triangulation.

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arXiv2010

Gauge theories from D7-branes over vanishing 4-cycles

We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.

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arXiv2010

Single-Sector Supersymmetry Breaking in Supersymmetric QCD

We construct examples of single-sector supersymmetry breaking based on simple deformations of supersymmetric QCD with (weakly) gauged flavor group. These theories are calculable in a weakly coupled Seiberg dual description. In these models, some of the particles in the first two generations of quarks and leptons are composites of the same strong dynamics which leads to dynamical supersymmetry breaking. Such models can explain the hierarchies of Yukawa couplings in the Standard Model, in a way that predictively correlates with the spectrum of SUSY-breaking soft terms.

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arXiv2010

Dynamical Supersymmetry Breaking, with Flavor

We explore calculable models with low-energy supersymmetry where the flavor hierarchy is generated by quark and lepton compositeness, and where the composites emerge from the same sector that dynamically breaks supersymmetry. The observed pattern of Standard Model fermion masses and mixings is obtained by identifying the various generations with composites of different dimension in the ultraviolet. These "single-sector" supersymmetry breaking models give rise to various spectra of soft masses which are, in many cases, quite distinct from what is commonly found in models of gauge or gravity mediation. In typical models which satisfy all flavor-changing neutral current constraints, both the first and second generation sparticles have masses of order 20 TeV, while the stop mass is near 1 TeV. In other cases, all sparticles obtain masses of order 1 TeV predominantly from gauge mediation, even though the first two generations are composite.

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arXiv2010

Phenomenological Models of Holographic Superconductors and Hall currents

We study general models of holographic superconductivity parametrized by four arbitrary functions of a neutral scalar field of the bulk theory. The models can accommodate several features of real superconductors, like arbitrary critical temperatures and critical exponents in a certain range, and perhaps impurities, boundary or thickness effects. We find analytical expressions for the critical exponents of the general model and show that they satisfy the Rushbrooke identity. An important subclass of models exhibits second order phase transitions. A study of the specific heat shows that general models can also describe holographic superconductors undergoing first, second and third (or higher) order phase transitions. We discuss how small deformations of the HHH model lead to the appearance of resonance peaks in the conductivity, which become narrower as the temperature is gradually decreased, without the need for tuning mass of the scalar to be close to the Breitenlohner-Freedman bound. Finally, we investigate the inclusion of a generalized "theta term" producing Hall effect without magnetic field.

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arXiv2010

Multi-Flux Warped Throats and Cascading Gauge Theories

We describe duality cascades and their infrared behavior for systems of D3-branes at singularities given by complex cones over del Pezzo surfaces (and related examples), in the presence of fractional branes. From the gauge field theory viewpoint, we show that D3-branes probing the infrared theory have a quantum deformed moduli space, given by a complex deformation of the initial geometry to a simpler one. This implies that for the dual supergravity viewpoint, the gauge theory strong infrared dynamics smoothes out the naked singularities of the recently constructed warped throat solutions with 3-form fluxes, describing the cascading RG flow of the gauge theory. This behavior thus generalizes the Klebanov-Strassler deformation of the conifold. We describe several explicit examples, including models with several scales of strong gauge dynamics. In the regime of widely separated scales, the dual supergravity solutions should correspond to throats with several radial regions with different exponential warp factors. These rich throat geometries are expected to have interesting applications in compactification and model building. Along our studies, we also construct explicit duality cascades for gauge theories with irrational R-charges, obtained from D-branes probing complex cones over dP1 and dP2.

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arXiv2009

A holographic approach to phase transitions

We provide a description of phase transitions at finite temperature in strongly coupled field theories using holography. For this purpose, we introduce a general class of gravity duals to superconducting theories that exhibit various types of phase transitions (first or second order with both mean and non-mean field behavior) as parameters in their Lagrangian are changed. Moreover the size and strength of the conductivity coherence peak can also be controlled. Our results suggest that certain parameters in the gravitational dual control the interactions responsible for binding the condensate and the magnitude of its fluctuations close to the transition.

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arXiv2009

A general class of holographic superconductors

We introduce a simple generalization of the basic holographic superconductor model in which the spontaneous breaking of a global U(1) symmetry occurs via the Stueckelberg mechanism. This more general setting allows tuning features such as the order of the transition. The physical vacuum of the condensed phase and the order of the transition are determined by a detailed analysis of the free energy of the system. For first order transitions, we identify a metastable phase above the critical temperature. In this case, the conductivity shows additional poles, thus suggesting that the condensate has internal structure. We comment on the possibility of obtaining second order phase transitions with non mean-field critical exponents.

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arXiv2009

M2-branes on Orbifolds of the Cone over Q^{1,1,1}

We study the N=2 supersymmetric Chern-Simons quiver gauge theory recently introduced in arXiv:0809.3237 to describe M2-branes on a cone over the well-known Sasaki-Einstein manifold Q^{1,1,1}. For Chern-Simons levels (k,k,-k,-k) we argue that this theory is dual to AdS_4 x Q^{1,1,1}/Z_k. We derive the Z_k orbifold action and show that it preserves geometrical symmetry U(1)_R x SU(2) x U(1), in agreement with the symmetry of the gauge theory. We analyze the simplest gauge invariant chiral operators, and show that they match Kaluza-Klein harmonics on AdS_4 x Q^{1,1,1}/Z_k. This provides a test of the gauge theory, and in particular of its sextic superpotential which plays an important role in restricting the spectrum of chiral operators. We proceed to study other quiver gauge theories corresponding to more complicated orbifolds of Q^{1,1,1}. In particular, we propose two U(N)^4 Chern-Simons gauge theories whose quiver diagrams are the same as in the 4d theories describing D3-branes on a complex cone over F_0, a Z_2 orbifold of the conifold (in 4d the two quivers are related by the Seiberg duality). The manifest symmetry of these gauge theories is U(1)_R x SU(2) x SU(2). We argue that these gauge theories at levels (k,k,-k,-k) are dual to AdS_4 x Q^{2,2,2}/Z_k. We exhibit calculations of the moduli space and of the chiral operator spectrum which provide support for this conjecture. We also briefly discuss a similar correspondence for AdS_4 x M^{3,2}/Z_k. Finally, we discuss resolutions of the cones and their dual gauge theories.

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arXiv2009

Holographic Gauge Mediation

We discuss gravitational backgrounds where supersymmetry is broken at the end of a warped throat, and the SUSY-breaking is transmitted to the Standard Model via gauginos which live in (part of) the bulk of the throat geometry. We find that the leading effect arises from splittings of certain "messenger mesons," which are adjoint KK-modes of the D-branes supporting the Standard Model gauge group. This picture is a gravity dual of a strongly coupled field theory where SUSY is broken in a hidden sector and transmitted to the Standard Model via a relative of semi-direct gauge mediation.

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arXiv2008

Towards M2-brane Theories for Generic Toric Singularities

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is the gauge theory associated with the cone over Q^{111}. For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models. Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.

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arXiv2008

SUSY breaking mediation by D-brane instantons

It is well known that D-brane instantons can generate contributions to the effective superpotential of gauge theories living on D-branes which are perturbatively forbidden by global U(1) symmetries. We extend this idea to theories with supersymmetry breaking, studying the effect of D-brane instantons stretched between the SUSY-breaking and visible sectors. Analogously to what happens in the SUSY case, this mechanism can give rise to perturbatively forbidden soft terms (among other effects). We introduce and discuss general properties of instanton mediation. We illustrate our ideas in simple Type IIB toroidal orientifolds. As a bi-product, we present a string theory realization of a Polonyi hidden sector.

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arXiv2008

N-ification of Forces: A Holographic Perspective on D-brane Model Building

We study geometric aspects of extensions of the supersymmetric standard model that exhibit a periodic duality cascade. Via the holographic correspondence, the growth of the gauge group rank towards the UV is interpreted as a gradual decompactification transition. We show that this class of models typically develop a duality wall in the UV, and present an efficient method for estimating the hierarchy between the on-set of the cascade and the formation of the wall. As an illustrative example, we study the model introduced by Cascales, Saad and Uranga in [14], which has an known geometric realization in terms of D-branes on an SPP/Z_3 singularity.

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arXiv2007

Dimers and Orientifolds

We introduce new techniques based on brane tilings to investigate D3-branes probing orientifolds of toric Calabi-Yau singularities. With these new tools, one can write down many orientifold models and derive the resulting low-energy gauge theories living on the D-branes. Using the set of ideas in this paper one recovers essentially all orientifolded theories known so far. Furthermore, new orientifolds of non-orbifold toric singularities are obtained. The possible applications of the tools presented in this paper are diverse. One particular application is the construction of models which feature dynamical supersymmetry breaking as well as the computation of D-instanton induced superpotential terms.

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arXiv2007

Metastable vacua and D-branes at the conifold

We consider quiver gauge theories arising on D-branes at simple Calabi-Yau singularities (quotients of the conifold). These theories have metastable supersymmetry breaking vacua. The field theoretic mechanism is basically the one exhibited by the examples of Intriligator, Seiberg and Shih in SUSY QCD. In a dual description, the SUSY breaking is captured by the presence of anti-branes. In comparison to our earlier related work, the main improvements of the present construction are that we can reach the free magnetic range of the SUSY QCD theory where the existence of the metastable vacua is on firm footing, and we can see explicitly how the small masses for the quark flavors (necessary to the existence of the SUSY breaking vacua) are dynamically stabilized. One crucial mass term is generated by a stringy instanton. Finally, our models naturally incorporate R-symmetry breaking in the non-supersymmetric vacuum, in a way similar to the examples of Kitano, Ooguri and Ookouchi.

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