Constitutive relations, off shell duality rotations and the hypergeometric form of Born-Infeld theory

We review equivalent formulations of nonlinear and higher derivatives theories of electromagnetism exhibiting electric-magnetic duality rotations symmetry. We study in particular on shell and off shell formulations of this symmetry, at the level of action functionals as well as of equations of motion. We prove the conjecture that the action functional leading to Born-Infeld nonlinear electromagnetism, that is duality rotation invariant off shell and that is known to be a root of an algebraic equation of fourth order, is a hypergeometric function.Comment: 20 pages. Contribution to the proceedings of the conference BUDS2013, Frascat

High-resolution transmission electron microscopy investigation of diffusion in metallic glass multilayer films

Lack of plasticity is one of the main disadvantages of metallic glasses. One of the solutions to this problem can be composite materials. Diffusion bonding is promising for composite fabrication. In the present work the diffusion process in glassy multilayer films was investigated. A combination of advanced transmission electron microscopy (TEM)methods and precision sputtering techniques allows visualization and study of diffusion in amorphous metallic layers with high resolution. Multilayered films were obtained by radio frequency sputter deposition of Zr-Cu and Zr-Pd. The multilayers were annealed under a high vacuum (10 −5 Pa)for 1 and 5 h at 400 °C, that is, well below the crystallization temperatures but very close to the glass-transition temperatures of both types of the glassy layer. The structural evolution in the deposited films was investigated by high-resolution transmission electron microscopy. It was observed that, despite the big differences in the atomic mass and size, Pd and Cu have similar diffusion coefficients. Surprisingly, 1 h of annealing results in formation of metastable copper nanocrystals in the Zr-Cu layers which, however, disappear after 5 h of annealing. This effect may be connected with nanovoid formation under a complex stress state evolving upon annealing, and is related to the exceptionally slow relaxation of the glassy layers sealed with a Ta overlayer.The authors acknowledge the financial support through the European Research Council under the ERC Advanced Grants INTELHYB (grant ERC-2013-ADG-340025) and ExtendGlass (grant ERC-2015-AdG-695487), the German Science Foundation (DFG) under the grant SO 1518/1-1, and the Ministry of Education and Science of the Russian Federation in the framework of the ‘Increase Competitiveness’ program of NUST ‘MISiS’ (№ К2-2014-013 and К2-2017-089)

Global aspects of the space of 6D N = 1 supergravities

We perform a global analysis of the space of consistent 6D quantum gravity theories with N = 1 supersymmetry, including models with multiple tensor multiplets. We prove that for theories with fewer than T = 9 tensor multiplets, a finite number of distinct gauge groups and matter content are possible. We find infinite families of field combinations satisfying anomaly cancellation and admitting physical gauge kinetic terms for T > 8. We find an integral lattice associated with each apparently-consistent supergravity theory; this lattice is determined by the form of the anomaly polynomial. For models which can be realized in F-theory, this anomaly lattice is related to the intersection form on the base of the F-theory elliptic fibration. The condition that a supergravity model have an F-theory realization imposes constraints which can be expressed in terms of this lattice. The analysis of models which satisfy known low-energy consistency conditions and yet violate F-theory constraints suggests possible novel constraints on low-energy supergravity theories.Comment: 41 pages, 1 figur

GCA in 2d

We make a detailed study of the infinite dimensional Galilean Conformal Algebra (GCA) in the case of two spacetime dimensions. Classically, this algebra is precisely obtained from a contraction of the generators of the relativistic conformal symmetry in 2d. Here we find quantum mechanical realisations of the (centrally extended) GCA by considering scaling limits of certain 2d CFTs. These parent CFTs are non-unitary and have their left and right central charges become large in magnitude and opposite in sign. We therefore develop, in parallel to the usual machinery for 2d CFT, many of the tools for the analysis of the quantum mechanical GCA. These include the representation theory based on GCA primaries, Ward identities for their correlation functions and a nonrelativistic Kac table. In particular, the null vectors of the GCA lead to differential equations for the four point function. The solution to these equations in the simplest case is explicitly obtained and checked to be consistent with various requirements.Comment: 45 pages; v2: 47 pages. Restructured introduction, minor corrections, added references. Journal versio

Moduli backreaction and supersymmetry breaking in string-inspired inflation models

We emphasize the importance of effects from heavy fields on supergravity models of inflation. We study, in particular, the backreaction of stabilizer fields and geometric moduli in the presence of supersymmetry breaking. Many effects do not decouple even if those fields are much heavier than the inflaton field. We apply our results to successful models of Starobinsky-like inflation and natural inflation. In most scenarios producing a plateau potential it proves difficult to retain the flatness of the potential after backreactions are taken into account. Some of them are incompatible with non-perturbative moduli stabilization. In natural inflation there exist a number of models which are not constrained by backreactions at all. In those cases the correction terms from heavy fields have the same inflaton-dependence as the uncorrected potential, so that inflation may be possible even for very large gravitino masses.Comment: 29 pages, 1 figure, comments added, subsection 2.3 added, published versio

Beyond Logarithmic Corrections to Cardy Formula

As shown by Cardy modular invariance of the partition function of a given unitary non-singular 2d CFT with left and right central charges c_L and c_R, implies that the density of states in a microcanonical ensemble, at excitations Delta and Delta-bar and in the saddle point approximation, is \rho_0(\Delta,\bar\Delta;c_L, c_R)=c_L c_R \exp(2\pi\sqrt{{c_L\Delta}/{6}})\exp(2\pi\sqrt{{c_R\bar\Delta}/{6}}). In this paper, we extend Cardy's analysis and show that in the saddle point approximation and up to contributions which are exponentially suppressed compared to the leading Cardy's result, the density of states takes the form \rho(\Delta,\bar\Delta; c_L,c_R)= f(c_L\Delta) f(c_R\bar\Delta)\rho_0(\Delta,\bar\Delta; c_L, c_R), for a function f(x) which we specify. In particular, we show that (i) \rho (\Delta,\bar\Delta; c_L, c_R) is the product of contributions of left and right movers and hence, to this approximation, the partition function of any modular invariant, non-singular unitary 2d CFT is holomorphically factorizable and (ii) \rho(\Delta,\bar\Delta; c_L, c_R)/(c_Lc_R) is only a function of $c_R\bar\Delta$ and $c_L\Delta$. In addition, treating \rho(\Delta,\bar\Delta; c_L, c_R) as the density of states of a microcanonical ensemble, we compute the entropy of the system in the canonical counterpart and show that the function f(x) is such that the canonical entropy, up to exponentially suppressed contributions, is simply given by the Cardy's result \ln\rho_0(\Delta,\bar\Delta; c_L, c_R).Comment: 30 pages, no figures; v2: minor improvements, one reference added, v3: minor corrections to match the published versio

Cosmological attractor models and higher curvature supergravity

We study cosmological \u3b1-attractors in superconformal/supergravity models, where \u3b1 is related to the geometry of the moduli space. For \u3b1 = 1 attractors [1] we present a generalization of the previously known manifestly superconformal higher curvature supergravity model [2]. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic \u3b1-models [3] interpolate between the attractor point at \u3b1 = 0 and generic chaotic inflation models at large \u3b1, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as the original theory or less, but at least one matter multiplet remains. In the context of these models, the detection of primordial gravity waves will provide information on the curvature of the inflaton submanifold of the K\ue4hler manifold, and we will learn if the inflaton is a fundamental matter multiplet, or can be replaced by a higher derivative curvature excitation. \ua9 2014 The Author(s)