Time-loops in Dirac materials, torsion and unconventional Supersymmetry
Alfredo Iorio, Pablo Pais
备注：
6 pages, 2 Figures; contribution to the Proceedings of the 40th International Conference on High Energy physics - ICHEP2020, July 28 - August 6, 2020, Prague, Czech Republic (virtual meeting)
We propose a scenario where the effects of dislocations, in bidimensional Dirac materials at low energies, can be described within a Dirac field theory by a vertex proportional to the totally antisymmetric component of the torsion generated by such dislocations. The well-known geometrical obstruction to have a nonzero torsion term of that kind in this two-dimensional settings is overcome through exotic time-loops, obtained from ingeniously manipulated particle-hole dynamics. If such torsion/dislocation is indeed present, a net flow of particles-antiparticles (holes) can be inferred and possibly measured. Finally, we comment on how these discoveries pave the way to a laboratory realization on Dirac materials of Unconventional Supersymmetry, as a top-down description of the $π$-electrons in backgrounds with a nonzero torsion.
We study the dimensional reduction of ten-dimensional super Yang-Mills theory in curved backgrounds with torsion. We examine the parallel spinor conditions and the constraints for the torsion parameters which preserve supersymmetry and gauge symmetry in four dimensions. In particular we examine the ten-dimensional Omega-background with the torsion which is identified with the R-symmetry Wilson line gauge fields. After the dimensional reduction, we obtain the Omega-deformed N=4 super Yang-Mills theory. Solving the parallel spinor conditions and the torsion constraints, we classify the deformed …
From a gauge $SU(2,2|2)$ model with broken supersymmetry, we construct an action for $SU(2)\times U(1)$ Yang-Mills theory coupled to gravity and matter. The connection components for AdS boosts and special conformal translations are auxiliary fields and their fixing reduces the theory to two distintive sectors: a vector-like gauge theory with general relativity and a chiral gauge theory where gravity drops out. We discuss some of the main classical features of the model such as the predicted tree level gauge couplings, cosmological constant value, mass-like terms and the Einstein equations.
In this paper we perform, in the spirit of the holographic correspondence, a particular asymptotic limit of N=2, AdS_4 supergravity to N=2 supergravity on a locally AdS_3 boundary. Our boundary theory enjoys OSp(2|2) x SO(1,2) invariance and is shown to contain the D=3 super-Chern Simons OSp(2|2) theory considered in [Alvarez:2011gd] and featuring "unconventional local supersymmetry". The model constructed in that reference describes the dynamics of a spin-1/2 Dirac field in the absence of spin 3/2 gravitini and was shown to be relevant for the description of graphene, near the Dirac points, f…
We analyze the conditions to have no-scale supersymmetry breaking solutions of type IIA and IIB supergravity compactified on manifolds of SU(3)-structure. The supersymmetry is spontaneously broken by the intrinsic torsion of the internal space. For type IIB orientifolds with O9 and O5-planes the mass of the gravitino is governed by the torsion class W_1, and the breaking is mediated through F-terms associated to descendants of the original N=2 hypermultiplets. For type IIA orientifolds with O6-planes we find two families of solutions, depending on whether the breaking is mediated exclusively b…
We derive a $2+1$ dimensional model with unconventional supersymmetry at the boundary of an ${\rm AdS}_4$ $\mathcal{N}$-extended supergravity, generalizing previous results. The (unconventional) extended supersymmetry of the boundary model is instrumental in describing, within a top-down approach, the electronic properties of graphene-like 2D materials at the two Dirac points, ${\bf K}$ and ${\bf K}'$. The two valleys correspond to the two independent sectors of the ${\rm OSp}(p|2)\times {\rm OSp}(q|2)$ boundary model in the $p=q$ case, which are related by a parity transformation. The Semenof…
Using (1,0) superfield methods, we determine the general scalar potential consistent with off-shell (p,0) supersymmetry and (1,1) supersymmetry in two-dimensional non-linear sigma models with torsion. We also present an extended superfield formulation of the (p,0) models and show how the (1,1) models can be obtained from the (1,1)-superspace formulation of the gauged, but massless, (1,1) sigma model.
We study the inclusion of fermionic degrees of freedom and ${\cal N}=1$ supersymmetry in 4-dimensional manifolds with arbitrary torsion and non-metricity tensors deforming the connection. We inspect the closure of local diffeomorphism, Lorentz and supersymmetric transformations on the vielbein and gravitino at leading order in fermions. The closure of a pair of supersymmetric transformations acting on the vielbein restricts the form of the spin connection. The dependency of the latter on the fundamental fields is exclusively given by the vielbein, up to Lorentz and/or diffeomorphisms brackets,…
We present a unified description of the quantum Hall effect in graphene on the basis of the 8-component Dirac Hamiltonian and the supersymmetric (SUSY) quantum mechanics. It is remarkable that the zero-energy state emerges because the Zeeman splitting is exactly as large as the Landau level separation, as implies that the SUSY is a good symmetry. For nonzero energy states, the up-spin state and the down-spin state form a supermultiplet possessing the spin SU(2) symmetry. We extend the Dirac Hamiltonian to include two indices $j_{\uparrow}$ and $j_{\downarrow}$, characterized by the dispersion …
We identify the auxiliary fields in the hypermultiplets of type IIB string theory compactified on a Calabi-Yau manifold, using a combination of worldsheet and supergravity techniques. The SUSY-breaking squark and gaugino masses in type IIB models depend on these auxiliary fields, which parametrize deformations away from a pure Calabi-Yau compactification to one with NS-NS 3-form flux and SU(3) x SU(3) structure. Worldsheet arguments show that such compactifications are generically globally nongeometric. Our results, combined with earlier results for type IIA compactifications, imply that these…
We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kahler, hyperkahler, and Calabi-Yau manifolds. The (2,2) supersymmetry guarantees that these spaces are genera…
The Dirac Hamiltonian formalism is applied to a system in $(2+1)$-dimensions consisting of a Dirac field $ψ$ minimally coupled to Chern-Simons $U(1)$ and $SO(2,1)$ connections, $A$ and $ω$, respectively. This theory is connected to a supersymmetric Chern-Simons form in which the gravitino has been projected out (unconventional supersymmetry) and, in the case of a flat background, corresponds to the low energy limit of graphene. The separation between first-class and second-class constraints is performed explicitly, and both the field equations and gauge symmetries of the Lagrangian formalism a…
Chiral symmetry breaking in models with unconventional supersymmetry
Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Centro de Estudios Científicos (CECs)（科学研究中心）；Centro de Ciencias Exactas & Departamento de Ciencias Básicas, Universidad del Bio-Bio（比奥比奥大学精确科学与基础科学系）
Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models with branes. As a non-compact example, we describe a family of metrics which correspond to deformations of the heterotic conifold by turning on H-flux. We then describe compact models which are gauge-invariant only at the quantum level. Our construction gives a generalization of symplectic reduction. The resulting spaces are non-Kahler analogues of familiar …
By analyzing super-torsion and brane super-cocycles, we derive a new duality in M-theory, which takes the form of a higher version of T-duality in string theory. This involves a new topology change mechanism abelianizing the 3-sphere associated with the C-field topology to the 517-torus associated with exceptional-generalized super-geometry. Finally we explain parity symmetry in M-theory within exceptional-generalized super-spacetime at the same level of spherical T-duality, namely as an isomorphism on 7-twisted cohomology.
We consider a general N=(2,2) non-linear sigma model with a torsion. We show that the consistency of N=(2,2) supersymmetry implies that the target manifold is necessary equipped with two (in general, different) Poisson structures. Finally we argue that the Poisson geometry of the target space is a characteristic feature of the sigma models with extended supersymmetry.
We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-structures and provide a comprehensive classification of static supersymmetric backgrounds in these theories. Generalised calibrations naturally appear since the geometries always admit NS or type I/heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. I…
In heterotic flux compactification with supersymmetry, three different connections with torsion appear naturally, all in the form $ω+a H$. Supersymmetry condition carries $a=-1$, the Dirac operator has $a=-1/3$, and higher order term in the effective action involves $a=1$. With a view toward the gauge sector, we explore the geometry with such torsions. After reviewing the supersymmetry constraints and finding a relation between the scalar curvature and the flux, we derive the squared form of the zero mode equations for gauge fermions. With $\d H=0$, the operator has a positive potential term, …
In supersymmetric extensions of the Standard Model, the observed particles come in fermion-boson pairs necessary for the realization of supersymmetry (SUSY). In spite of the expected abundance of super-partners for all the known particles, not a single supersymmetric pair has been reported to date. Although a hypothetical SUSY breaking mechanism, operating at high energy inaccessible to current experiments cannot be ruled out, this reduces SUSY's predictive power and it is unclear whether SUSY, in its standard form, can help reducing the remaining puzzles of the standard model (SM). Here we ar…
We consider Shiraishi's metrics on the moduli space of extreme black holes. We interpret the simplification in the pattern of N-body interactions that he observed in terms of the recent picture of black holes in four and five dimensions as composites, made up of intersecting branes. We then show that the geometry of the moduli space of a class of black holes in five and nine dimensions is hyper-Kähler with torsion, and octonionic-Kähler with torsion, respectively. For this, we examine the geometry of point particle models with extended world-line supersymmetry and show that both of the above g…
We present the electronic properties of massless Dirac fermions characterized by geometry and topology on a graphene sheet in this chapter. Topological effects can be elegantly illuminated by the Atiyah-Singer index theorem. It leads to a topological invariant under deformations on the Dirac operator and plays an essential role in formulating supersymmetric quantum mechanics over twisted Dolbeault complex caused by the topological deformation of the lattice in a graphene system. Making use of the G index theorem and a high degree of symmetry, we study deformed energy eigenvalues in graphene. T…
We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the alpha'-exact statistical entropies obtained from microstate counting (D=4) and AdS/CFT correspondence (D=5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R^2-truncated (four-derivative) action…
Non-trivial supergeneralization of the Kerr-Newman solution is considered as representing a combined model of the Kerr-Newman spinning particle and superparticle. We show that the old problem of obtaining non-trivial super black hole solutions can be resolved in supergravity broken by Goldstone fermion. Non-linear realization of broken N=2 supersymmetry specific for the Kerr geometry is considered and some examples of the super-Kerr geometries generated by Goldstone fermion are analyzed. The resulting geometries acquire torsion, Rarita-Schwinger field and extra wave contributions to metric and…
Based on recent discussions on the so-called unconventional supersymmetry, we propose a 5D Chern-Simons AdS-$\mathcal{N}$-SUGRA formulation without gravitino fields and show that a residual local SUSY is preserved. We explore the properties of CS theories to find a solution to the field equations in a 5D manifold. With a Randall-Sundrum-type ansatz, we show that this particular dimensional reduction is compatible with SUSY, and some classes of 4D solutions are then analyzed.
We discuss a 1+2 dimensional model with unconventional supersymmetry at the boundary of an AdS${}_4$, \,$\mathcal{N}$-extended supergravity. The resulting features of the supersymmetric boundary open the possibility of describing the electronic properties of graphene-like 2D materials at the Dirac points \textbf{K} and \textbf{K'}, exploiting a top-down approach. The Semenoff and Haldane-type masses entering the corresponding Dirac equations can be then extrapolated from the geometric parameters of the model describing the substrate.
We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a $(3+1)$-dimensional theory, with nonzero torsion, with spatiotemporal gauge group $SO(3,1)$, locally isomorphic to the Lorentz group in $(3+1)$ dimensions, or to the de Sitter group in $(2+1)$ dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry wit…
