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Springer

Received: October Revised: November Accepted: November Published: January

15, 15, 24, 15,

2019 2019 2019 2020

L. Andrianopoli,a,b,e B.L. Cerchiai,a,b,c R. D’Auria,a,e A. Gallerati,a,b R. Noris,a,b M. Trigiantea,b,e and J. Zanellid a

Politecnico di Torino, Dipartimento DISAT, Corso Duca degli Abruzzi 24, Torino 10129, Italy b Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Torino, via Pietro Giuria 1, Torino 10125, Italy c Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Piazza del Viminale 1, Roma 00184, Italy d Centro de Estudios Cient´ıficos (CECs), Av. Arturo Prat 514, Valdivia, Chile e Arnold-Regge Center, via P. Giuria 1, Torino 10125, Italy

E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We derive a 2+1 dimensional model with unconventional supersymmetry at the boundary of an AdS4 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, K and K0 . The two valleys correspond to the two independent sectors of the OSp(p|2) × OSp(q|2) boundary model in the p = q case, which are related by a parity transformation. The Semenoff and Haldane-type masses entering the corresponding Dirac equations are identified with the torsion parameters of the substrate in the model. Keywords: Chern-Simons Theories, Holography and condensed matter physics (AdS/ CMT), Supergravity Models ArXiv ePrint: 1910.03508

c The Authors. Open Access, Article funded by SCOAP3 .

https://doi.org/10.1007/JHEP01(2020)084

JHEP01(2020)084

N -extended D = 4 supergravity, unconventional SUSY and graphene

Contents 1 Introduction

1

2 Ach´ ucarro-Townsend D = 3 theory from AdS4 supergravity 2.1 Boundary limit 2.2 Reflection transformations and the symmetric case p = q

4 5 8 9 9 12

4 Interpretation in terms of graphene-like 2D materials 4.1 The p = q case and the K, K0 Dirac points 4.1.1 Microscopic interpretation 4.2 A different model for graphene

14 16 18 19

5 Concluding remarks

20

A OSp(N |4) algebra and conventions

21

B Microscopic description for graphene-like systems B.1 Massive deformations

23 23

1

Introduction

Chern-Simons theories including gravity and matter in three dimensions developed three decades ago by Ach´ ucarro and Townsend [1], have been shown to exhibit interesting features [2, 3], particularly in connection with the holographic correspondence [4–6]. Our interest here focuses on the Ach´ ucarro-Townsend (AT) theory, following the Ansatz proposed in [7, 8] (referred to as the AVZ model in the sequel). The AVZ model consists of a Chern-Simons system in 2 + 1 dimensions for the supergroup OSp(2|2). It is an effective theory for a massive spin-1/2 fermion, generically defined on a curved geometry and minimally coupled to the backgrou