Wall Crossing, Quivers and Crystals

We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1 dimensional quiver gauge theory that describes the dynamics of the branes at low energies. The results of Kontsevich and Soibelman predict how the degeneracies change. We argue that Seiberg dualities of the quiver gauge theories, which change the basis of BPS states, correspond to crossing the "walls of the second kind." There is a large class of examples, including local del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by melting crystal configurations. We show that the melting crystals that arise are a discretization of the Calabi-Yau geometry. The shape of the crystal is determined by the Calabi-Yau geometry and the background B-field, and its microscopic structure by the quiver Q. We prove that the BPS degeneracies computed from Q and Q' are related by the Kontsevich Soibelman formula, using a geometric realization of the Seiberg duality in the crystal. We also show that, in the limit of infinite B-field, the combinatorics of crystals arising from the quivers becomes that of the topological vertex. We thus re-derive the Gromov-Witten/Donaldson-Thomas correspondence

On the Classification of Brane Tilings

We present a computationally efficient algorithm that can be used to generate all possible brane tilings. Brane tilings represent the largest class of superconformal theories with known AdS duals in 3+1 and also 2+1 dimensions and have proved useful for describing the physics of both D3 branes and also M2 branes probing Calabi-Yau singularities. This algorithm has been implemented and is used to generate all possible brane tilings with at most 6 superpotential terms, including consistent and inconsistent brane tilings. The collection of inconsistent tilings found in this work form the most comprehensive study of such objects to date.Comment: 33 pages, 12 figures, 15 table

Superconformal Block Quivers, Duality Trees and Diophantine Equations

We generalize previous results on N = 1, (3 + 1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice

The singlet scalar as FIMP dark matter

The singlet scalar model is a minimal extension of the Standard Model that can explain the dark matter. We point out that in this model the dark matter constraint can be satisfied not only in the already considered WIMP regime but also, for much smaller couplings, in the Feebly Interacting Massive Particle (FIMP) regime. In it, dark matter particles are slowly produced in the early Universe but are never abundant enough to reach thermal equilibrium or annihilate among themselves. This alternative framework is as simple and predictive as the WIMP scenario but it gives rise to a completely different dark matter phenomenology. After reviewing the calculation of the dark matter relic density in the FIMP regime, we study in detail the evolution of the dark matter abundance in the early Universe and the predicted relic density as a function of the parameters of the model. A new dark matter compatible region of the singlet model is identified, featuring couplings of order 10^-11 to 10^-12 for singlet masses in the GeV to TeV range. As a consequence, no signals at direct or indirect detection experiments are expected. The relevance of this new viable region for the correct interpretation of recent experimental bounds is emphasized.Comment: 12 pages, 6 figure

Demagnetization of Quantum Dot Nuclear Spins: Breakdown of the Nuclear Spin Temperature Approach

The physics of interacting nuclear spins arranged in a crystalline lattice is typically described using a thermodynamic framework: a variety of experimental studies in bulk solid-state systems have proven the concept of a spin temperature to be not only correct but also vital for the understanding of experimental observations. Using demagnetization experiments we demonstrate that the mesoscopic nuclear spin ensemble of a quantum dot (QD) can in general not be described by a spin temperature. We associate the observed deviations from a thermal spin state with the presence of strong quadrupolar interactions within the QD that cause significant anharmonicity in the spectrum of the nuclear spins. Strain-induced, inhomogeneous quadrupolar shifts also lead to a complete suppression of angular momentum exchange between the nuclear spin ensemble and its environment, resulting in nuclear spin relaxation times exceeding an hour. Remarkably, the position dependent axes of quadrupolar interactions render magnetic field sweeps inherently non-adiabatic, thereby causing an irreversible loss of nuclear spin polarization.Comment: 15 pages, 3 figure

Strain-controlled criticality governs the nonlinear mechanics of fibre networks

Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of connections between nodes exceeds the isostatic threshold are networks stable (Maxwell, J. C., Philosophical Magazine 27, 294 (1864)). Upon increasing the connectivity through this point, such networks undergo a mechanical phase transition from a floppy to a rigid phase. However, even sub-isostatic networks become rigid when subjected to sufficiently large deformations. To study this strain-controlled transition, we perform a combination of computational modeling of fibre networks and experiments on networks of type I collagen fibers, which are crucial for the integrity of biological tissues. We show theoretically that the development of rigidity is characterized by a strain-controlled continuous phase transition with signatures of criticality. Our experiments demonstrate mechanical properties consistent with our model, including the predicted critical exponents. We show that the nonlinear mechanics of collagen networks can be quantitatively captured by the predictions of scaling theory for the strain-controlled critical behavior over a wide range of network concentrations and strains up to failure of the material

New Constraints (and Motivations) for Abelian Gauge Bosons in the MeV-TeV Mass Range

We survey the phenomenological constraints on abelian gauge bosons having masses in the MeV to multi-GeV mass range (using precision electroweak measurements, neutrino-electron and neutrino-nucleon scattering, electron and muon anomalous magnetic moments, upsilon decay, beam dump experiments, atomic parity violation, low-energy neutron scattering and primordial nucleosynthesis). We compute their implications for the three parameters that in general describe the low-energy properties of such bosons: their mass and their two possible types of dimensionless couplings (direct couplings to ordinary fermions and kinetic mixing with Standard Model hypercharge). We argue that gauge bosons with very small couplings to ordinary fermions in this mass range are natural in string compactifications and are likely to be generic in theories for which the gravity scale is systematically smaller than the Planck mass - such as in extra-dimensional models - because of the necessity to suppress proton decay. Furthermore, because its couplings are weak, in the low-energy theory relevant to experiments at and below TeV scales the charge gauged by the new boson can appear to be broken, both by classical effects and by anomalies. In particular, if the new gauge charge appears to be anomalous, anomaly cancellation does not also require the introduction of new light fermions in the low-energy theory. Furthermore, the charge can appear to be conserved in the low-energy theory, despite the corresponding gauge boson having a mass. Our results reduce to those of other authors in the special cases where there is no kinetic mixing or there is no direct coupling to ordinary fermions, such as for recently proposed dark-matter scenarios.Comment: 49 pages + appendix, 21 figures. This is the final version which appears in JHE

Seiberg duality for Chern-Simons quivers and D-brane mutations

Chern-Simons quivers for M2-branes at Calabi-Yau singularities are best understood as the low energy theory of D2-branes on a dual type IIA background. We show how the D2-brane point of view naturally leads to three dimensional Seiberg dualities for Chern-Simons quivers with chiral matter content: They arise from a change of brane basis (or mutation), in complete analogy with the better known Seiberg dualities for D3-brane quivers. This perspective reproduces the known rules for Seiberg dualities in Chern-Simons-Yang-Mills theories with unitary gauge groups. We provide explicit examples of dual theories for the quiver dual to the Y^{p,q}(CP^2) geometries. We also comment on the string theory derivation of CS quivers dual to massive type IIA geometries.Comment: 32 pages+appendix; v2: added a referenc

D-branes Wrapped on Fuzzy del Pezzo Surfaces

We construct classical solutions in quiver gauge theories on D0-branes probing toric del Pezzo singularities in Calabi-Yau manifolds. Our solutions represent D4-branes wrapped around fuzzy del Pezzo surfaces. We study the fluctuation spectrum around the fuzzy CP^2 solution in detail. We also comment on possible applications of our fuzzy del Pezzo surfaces to the fuzzy version of F-theory, dubbed F(uzz) theory.Comment: 1+42 pages, 9 figures v2: references added v3: statements on the structure of the Yukawa couplings weakened. published versio

The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories

We consider N = 3 supersymmetric Chern-Simons gauge theories with product unitary and orthosymplectic groups and bifundamental and fundamental fields. We study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov matrix model. The saddlepoint equations in a large N limit lead to a constraint that the long range forces between the eigenvalues must cancel; the resulting quiver theories are of affine Dynkin type. We introduce a folding/unfolding trick which lets us, at the level of the large N matrix model, (i) map quivers with orthosymplectic groups to those with unitary groups, and (ii) obtain non-simply laced quivers from the corresponding simply laced quivers using a Z_2 outer automorphism. The brane configurations of the quivers are described in string theory and the folding/unfolding is interpreted as the addition/subtraction of orientifold and orbifold planes. We also relate the U(N) quiver theories to the affine ADE quiver matrix models with a Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in 2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions.Comment: 30 pages, 5 figure