Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

The Full Two-Loop R-parity Violating Renormalization Group Equations for All Minimal Supersymmetric Standard Model Couplings

We present the full two-loop $\beta$-functions for the minimal supersymmetric standard model couplings, extended to include R-parity violating couplings through explicit R-parity violation

2d Gauge Theories and Generalized Geometry

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure $D \subset \mathbb{T}M$ (or, more generally, the choide of a "small Dirac-Rinehart sheaf" $\cal{D}$), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: A gauging of $\mathfrak{g}$ of a standard sigma model with Wess-Zumino term exists, \emph{iff} there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid $M \times \mathfrak{g}\to M$ into $D\to M$ (or the algebraic analogue of the morphism in the case of $\cal{D}$). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense.Comment: 22 pages, 2 figures; To appear in Journal of High Energy Physic

Structures and waves in a nonlinear heat-conducting medium

The paper is an overview of the main contributions of a Bulgarian team of researchers to the problem of finding the possible structures and waves in the open nonlinear heat conducting medium, described by a reaction-diffusion equation. Being posed and actively worked out by the Russian school of A. A. Samarskii and S.P. Kurdyumov since the seventies of the last century, this problem still contains open and challenging questions.Comment: 23 pages, 13 figures, the final publication will appear in Springer Proceedings in Mathematics and Statistics, Numerical Methods for PDEs: Theory, Algorithms and their Application

The Higgs as a Probe of Supersymmetric Extra Sectors

We present a general method for calculating the leading contributions to h -> gg and h -> gamma gamma in models where the Higgs weakly mixes with a nearly supersymmetric extra sector. Such mixing terms can play an important role in raising the Higgs mass relative to the value expected in the MSSM. Our method applies even when the extra sector is strongly coupled, and moreover does not require a microscopic Lagrangian description. Using constraints from holomorphy we fix the leading parametric form of the contributions to these Higgs processes, including the Higgs mixing angle dependence, up to an overall coefficient. Moreover, when the Higgs is the sole source of mass for a superconformal sector, we show that even this coefficient is often calculable. For appropriate mixing angles, the contribution of the extra states to h -> gg and h -> gamma gamma can vanish. We also discuss how current experimental limits already lead to non-trivial constraints on such models. Finally, we provide examples of extra sectors which satisfy the requirements necessary to use the holomorphic approximation.Comment: v4: 34 pages, 2 figures, typo corrected and clarification adde

Bounds on SCFTs from Conformal Perturbation Theory

The operator product expansion (OPE) in 4d (super)conformal field theory is of broad interest, for both formal and phenomenological applications. In this paper, we use conformal perturbation theory to study the OPE of nearly-free fields coupled to SCFTs. Under fairly general assumptions, we show that the OPE of a chiral operator of dimension $\Delta = 1+\epsilon$ with its complex conjugate always contains an operator of dimension less than $2 \Delta$. Our bounds apply to Banks-Zaks fixed points and their generalizations, as we illustrate using several examples.Comment: 36 pages; v2: typos fixed, minor change

Probing Colored Particles with Photons, Leptons, and Jets

If pairs of new colored particles are produced at the Large Hadron Collider, determining their quantum numbers, and even discovering them, can be non-trivial. We suggest that valuable information can be obtained by measuring the resonant signals of their near-threshold QCD bound states. If the particles are charged, the resulting signatures include photons and leptons and are sufficiently rich for unambiguously determining their various quantum numbers, including the charge, color representation and spin, and obtaining a precise mass measurement. These signals provide well-motivated benchmark models for resonance searches in the dijet, photon+jet, diphoton and dilepton channels. While these measurements require that the lifetime of the new particles be not too short, the resulting limits, unlike those from direct searches for pair production above threshold, do not depend on the particles' decay modes. These limits may be competitive with more direct searches if the particles decay in an obscure way.Comment: 39 pages, 9 figures; v2: more recent searches include

Precision Gauge Unification from Extra Yukawa Couplings

We investigate the impact of extra vector-like GUT multiplets on the predicted value of the strong coupling. We find in particular that Yukawa couplings between such extra multiplets and the MSSM Higgs doublets can resolve the familiar two-loop discrepancy between the SUSY GUT prediction and the measured value of alpha_3. Our analysis highlights the advantages of the holomorphic scheme, where the perturbative running of gauge couplings is saturated at one loop and further corrections are conveniently described in terms of wavefunction renormalization factors. If the gauge couplings as well as the extra Yukawas are of O(1) at the unification scale, the relevant two-loop correction can be obtained analytically. However, the effect persists also in the weakly-coupled domain, where possible non-perturbative corrections at the GUT scale are under better control.Comment: 26 pages, LaTeX. v6: Important early reference adde

A slice of AdS_5 as the large N limit of Seiberg duality

A slice of AdS_5 is used to provide a 5D gravitational description of 4D strongly-coupled Seiberg dual gauge theories. An (electric) SU(N) gauge theory in the conformal window at large N is described by the 5D bulk, while its weakly coupled (magnetic) dual is confined to the IR brane. This framework can be used to construct an N = 1 MSSM on the IR brane, reminiscent of the original Randall-Sundrum model. In addition, we use our framework to study strongly-coupled scenarios of supersymmetry breaking mediated by gauge forces. This leads to a unified scenario that connects the extra-ordinary gauge mediation limit to the gaugino mediation limit in warped space.Comment: 47 Pages, axodraw4j.st

Numerical instability of the Akhmediev breather and a finite-gap model of it

In this paper we study the numerical instabilities of the NLS Akhmediev breather, the simplest space periodic, one-mode perturbation of the unstable background, limiting our considerations to the simplest case of one unstable mode. In agreement with recent theoretical findings of the authors, in the situation in which the round-off errors are negligible with respect to the perturbations due to the discrete scheme used in the numerical experiments, the split-step Fourier method (SSFM), the numerical output is well-described by a suitable genus 2 finite-gap solution of NLS. This solution can be written in terms of different elementary functions in different time regions and, ultimately, it shows an exact recurrence of rogue waves described, at each appearance, by the Akhmediev breather. We discover a remarkable empirical formula connecting the recurrence time with the number of time steps used in the SSFM and, via our recent theoretical findings, we establish that the SSFM opens up a vertical unstable gap whose length can be computed with high accuracy, and is proportional to the inverse of the square of the number of time steps used in the SSFM. This neat picture essentially changes when the round-off error is sufficiently large. Indeed experiments in standard double precision show serious instabilities in both the periods and phases of the recurrence. In contrast with it, as predicted by the theory, replacing the exact Akhmediev Cauchy datum by its first harmonic approximation, we only slightly modify the numerical output. Let us also remark, that the first rogue wave appearance is completely stable in all experiments and is in perfect agreement with the Akhmediev formula and with the theoretical prediction in terms of the Cauchy data.Comment: 27 pages, 8 figures, Formula (30) at page 11 was corrected, arXiv admin note: text overlap with arXiv:1707.0565