Holographic RG flows for Kondo-like impurities

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Springer

Received: February 17, 2020 Accepted: April 17, 2020 Published: May 18, 2020

Holographic RG flows for Kondo-like impurities

a

Institut f¨ ur Theoretische Physik und Astrophysik, Julius-Maximilians-Universit¨ at W¨ urzburg, Am Hubland, 97074 W¨ urzburg, Germany b W¨ urzburg-Dresden Cluster of Excellence ct.qmat, Julius-Maximilians-Universit¨ at W¨ urzburg, Am Hubland, 97074 W¨ urzburg, Germany

E-mail: [email protected], [email protected], [email protected] Abstract: Boundary, defect, and interface RG flows, as exemplified by the famous Kondo model, play a significant role in the theory of quantum fields. We study in detail the holographic dual of a non-conformal supersymmetric impurity in the D1/D5 CFT. Its RG flow bears similarities to the Kondo model, although unlike the Kondo model the CFT is strongly coupled in the holographic regime. The interface we study preserves d = 1 N = 4 supersymmetry and flows to conformal fixed points in both the UV and IR. The interface’s UV fixed point is described by d = 1 fermionic degrees of freedom, coupled to a gauge connection on the CFT target space that is induced by the ADHM construction. We briefly discuss its field-theoretic properties before shifting our focus to its holographic dual. We analyze the supergravity dual of this interface RG flow, first in the probe limit and then including gravitational backreaction. In the probe limit, the flow is realized by the puffing up of probe branes on an internal S3 via the Myers effect. We further identify the backreacted supergravity configurations dual to the interface fixed points. These supergravity solutions provide a geometric realization of critical screening of the defect degrees of freedom. This critical screening arises in a way similar to the original Kondo model. We compute the g-factor both in the probe brane approximation and using backreacted supergravity solutions, and show that it decreases from the UV to the IR as required by the g-theorem. Keywords: AdS-CFT Correspondence, Gauge-gravity correspondence, Holography and condensed matter physics (AdS/CMT) ArXiv ePrint: 2001.04991

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

https://doi.org/10.1007/JHEP05(2020)075

JHEP05(2020)075

Johanna Erdmenger,a,b Charles M. Melby-Thompsona and Christian Northea,b

Contents 1 Introduction

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2 Kondo-like defects in AdS/CFT

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4 Interfaces in the D1/D5 system 4.1 SUSY interfaces in the D1/D5 system 4.2 Holographic realization 4.3 Non-abelian description of the interface flow 4.4 D3-brane description of the interface flow

14 15 16 18 21

5 Backreacted supergravity dual of the interface fixed points 5.1 Supergravity duals of conformal interfaces in CFT2 5.1.1 Regularity constraints 5.1.2 Trivial interface: the D1/D5 geometry 5.2 Backreacted defect solutions 5.2.1 F1/D1 interface (UV) 5.2.2 D3 interface (IR) 5.3 Matching to the RG flow’s fixed points

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6 Interface entropy 6.1 Probe brane computation 6.2 Supergravity computation