Holographic Floquet states in low dimensions
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Springer
Received: July 29, 2020 Accepted: September 4, 2020 Published: October 1, 2020
Holographic Floquet states in low dimensions
Departamento de F´ısica de Part´ıculas, Universidade de Santiago de Compostela, and Instituto Galego de F´ısica de Altas Enerx´ıas (IGFAE), E-15782 Santiago de Compostela, Spain
E-mail: [email protected], [email protected], [email protected] Abstract: We study the response of a (2+1)-dimensional gauge theory to an external rotating electric field. In the strong coupling regime such system is formulated holographically in a top-down model constructed by intersecting D3- and D5-branes along 2+1 dimensions, in the quenched approximation, in which the D5-brane is a probe in the AdS5 × S5 geometry. The system has a non-equilibrium phase diagram with conductive and insulator phases. The external driving induces a rotating current due to vacuum polarization (in the insulator phase) and to Schwinger effect (in the conductive phase). For some particular values of the driving frequency the external field resonates with the vector mesons of the model and a rotating current can be produced even in the limit of vanishing driving field. These features are in common with the (3+1) dimensional setup based on the D3-D7 brane model [26, 27] and hint on some interesting universality. We also compute the conductivities paying special attention to the photovoltaic induced Hall effect, which is only present for massive charged carriers. In the vicinity of the Floquet condensate the optical Hall coefficient persists at zero driving field, signalling time reversal symmetry breaking. Keywords: AdS-CFT Correspondence, D-branes ArXiv ePrint: 2007.12115
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)013
JHEP10(2020)013
Ana Garbayo, Javier Mas and Alfonso V. Ramallo
Contents 1 Introduction
2
2 Setup and ansatz 2.1 Boundary conditions
4 7 8 8 9 9 10
4 Phase diagram
11
5 Analytic solutions 5.1 Massless embeddings 5.2 High frequency limit
15 15 17
6 Conductivities 6.1 AC conductivities 6.2 DC conductivities 6.3 Massless limit
18 22 24 27
7 Summary and outlook
27
A Regularity conditions A.1 Large frequency A.2 Small frequency
29 30 30
B Small mass solutions
30
C Embeddings in the linearized approximation C.1 Minkowski embeddings C.2 Black hole embeddings C.3 Critical embeddings
33 33 35 38
D Conductivities in the massless case
39
E More on optical conductivities
42
–1–
JHEP10(2020)013
3 Types of embeddings 3.1 Black hole embeddings 3.2 Minkowski embeddings 3.3 Critical embeddings 3.4 Effective metric
1
Introduction
Ex + i Ey = E eiΩt .
(1.1)
We will address this problem in the context of the holographic AdS/CFT correspondence [21] (see [22–25] for reviews), and will follow closely the pioneering work in refs. [26, 27] in their study of (3 + 1)-dimensional systems. In the first of these two references, the authors studied the massless D3-D7 flavour system and computed the artificially induced Hall conductivity. In the second
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