Friedel Oscillations and Horizon Charge in 1D Holographic Liquids Nabil Iqbal Kavli Institute for Theoretical Physics 1207.4208 In collaboration with Thomas.

Slides:



Advertisements
Similar presentations
On d=3 Yang-Mills-Chern- Simons theories with “fractional branes” and their gravity duals Ofer Aharony Weizmann Institute of Science 14 th Itzykson Meeting.
Advertisements

Gauge/gravity and condensed matter
Holographic Superconductors with Higher Curvature Corrections Sugumi Kanno (Durham) work w/ Ruth Gregory (Durham) Jiro Soda (Kyoto) arXiv: , to.
Topological current effect on hQCD at finite density and magnetic field Pablo A. Morales Work in collaboration with Kenji Fukushima Based on Phys. Rev.
Singularities in String Theory Hong Liu Massachusetts Institute of Technology ICHEP 04 Beijing.
Chanyong Park 35 th Johns Hopkins Workshop ( Budapest, June 2011 ) Based on Phys. Rev. D 83, (2011) arXiv : arXiv :
3rd International Workshop On High Energy Physics In The LHC Era.
Inching Towards Strange Metallic Holography David Tong Imperial, Feb 2010 Based on “Towards Strange Metallic Holography”, with Sean Hartnoll,
Microscopic entropy of the three-dimensional rotating black hole of BHT massive gravity of BHT massive gravity Ricardo Troncoso Ricardo Troncoso In collaboration.
Entanglement in Quantum Critical Phenomena, Holography and Gravity Dmitri V. Fursaev Joint Institute for Nuclear Research Dubna, RUSSIA Banff, July 31,
QCD – from the vacuum to high temperature an analytical approach an analytical approach.
AdS/CFT-QCD-CMT Yi NTHU April 8 th, 2010.
Dual gravity approach to near-equilibrium processes in strongly coupled gauge theories Andrei Starinets Hadrons and Strings Trento July 20, 2006 Perimeter.
Fluctuations and Correlations of Conserved Charges in QCD at Finite Temperature with Effective Models Wei-jie Fu, ITP, CAS Collaborated with Prof. Yu-xin.
Field Theory: The Past 25 Years Nathan Seiberg (IAS) The Future of Physics October, 2004 A celebration of 25 Years of.
PHY 042: Electricity and Magnetism Introduction Prof. Pierre-Hugues Beauchemin.
Holographic duality for condensed matter physics From To , KITPC, Beijing, China Kyung Kiu Kim(GIST;Gwangju Institute of Science and.
A CRITICAL POINT IN A ADS/QCD MODEL Wu, Shang-Yu (NCTU) in collaboration with He, Song, Yang, Yi and Yuan, Pei-Hung , to appear in JHEP
Effective Polyakov line actions from the relative weights method Jeff Greensite and Kurt Langfeld Lattice 2013 Mainz, Germany July 2013 Lattice 2013 Mainz,
The Quantum Space-Time Juan Maldacena Institute for Advanced Study 25 th Solvay Conference October 2011.
Why General Relativity is like a High Temperature Superconductor Gary Horowitz UC Santa Barbara G.H., J. Santos, D. Tong, , and to appear Gary.
HOLOGRAPHY, DIFFEOMORHISMS, AND THE CMB Finn Larsen University of Michigan Quantum Black Holes at OSU Ohio Center for Theoretical Science September
Cosmological Vacuum Selection and Meta-Stable Susy Breaking Ioannis Dalianis IFT-University of Warsaw.
Holographic Description of Quantum Black Hole on a Computer Yoshifumi Hyakutake (Ibaraki Univ.) Collaboration with M. Hanada ( YITP, Kyoto ), G. Ishiki.
Holographic Superconductors
An introduction to the Gravity/Fluid correspondence and its applications Ya-Peng Hu College of Science, Nanjing University of Aeronautics and Astronautics,
Louisville March 22, 2006 Andrew Chamblin Memorial An AdS Thermal Properties of Strongly Coupled Gauge Theories with Fundamental Matter from Gauge/Gravity.
Constraining theories with higher spin symmetry Juan Maldacena Institute for Advanced Study Based on: and by J. M. and A. Zhiboedov.
General Relativity and the Cuprates Gary Horowitz UC Santa Barbara GH, J. Santos, D. Tong, , GH and J. Santos, Gary Horowitz.
Constraining theories with higher spin symmetry Juan Maldacena Institute for Advanced Study Based on & to appearhttp://arxiv.org/abs/
QGP and Hadrons in Dense medium: a holographic 2nd ATHIC based on works with X. Ge, Y. Matsuo, F. Shu, T. Tsukioka(APCTP), archiv:
Spin-statistics theorem As we discussed in P301, all sub-atomic particles with which we have experience have an internal degree of freedom known as intrinsic.
Finite N Index and Angular Momentum Bound from Gravity “KEK Theory Workshop 2007” Yu Nakayama, 13 th. Mar (University of Tokyo) Based on hep-th/
Entanglement Entropy in Holographic Superconductor Phase Transitions Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences (April 17,
AdS/CFT Correspondence and Entanglement Entropy Tadashi Takayanagi (Kyoto U.) Based on hep-th/ [Phys.Rev.Lett.96(2006)181602] hep-th/ [JHEP.
HIGHER SPIN SUPERGRAVITY DUAL OF KAZAMA-SUZUKI MODEL Yasuaki Hikida (Keio University) Based on JHEP02(2012)109 [arXiv: [hep-th]]; arXiv:
On Fuzzball conjecture Seiji Terashima (YITP, Kyoto) based on the work (PRD (2008), arXiv: ) in collaboration with Noriaki Ogawa (YITP)
Holographic Superconductors from Gauss-Bonnet Gravity Rong-Gen Cai Institute of Theoretical Physics Chinese Academy of Sciences (May 7, 2012) 2012 海峡两岸粒子物理和宇宙学研讨会,
Holographic Models for High-Tc superconductors Jiunn-Wei Chen (NTU) w/ Ying-Jer Kao, Debaprasad Maity, Wen-Yu Wen and Chen-Pin Yeh (talk largely based.
Transport coefficients in strongly coupled gauge theories: insights from string theory Andrei Starinets Perimeter Institute for Theoretical Physics.
II Russian-Spanish Congress “Particle and Nuclear Physics at all scales and Cosmology”, Saint Petersburg, Oct. 4, 2013 RECENT ADVANCES IN THE BOTTOM-UP.
Strong coupling problems in condensed matter and the AdS/CFT correspondence HARVARD arXiv: Reviews: Talk online: sachdev.physics.harvard.edu arXiv:
The fast life of holographic mesons Aninda Sinha Perimeter Institute, Canada. with Robert Myers arXiv:0802.nnnn Quark Matter 2008, Jaipur, India.
Comments on entanglement entropy in the dS/CFT correspondence Yoshiki Sato ( Kyoto U. ) PRD 91 (2015) 8, [arXiv: ] 9th July.
Topology induced emergent dynamic gauge theory in an extended Kane-Mele-Hubbard model Xi Luo January 5, 2015 arXiv:
Holographic QCD in the medium
Strings, Gravity and the Large N Limit of Gauge Theories Juan Maldacena Institute for Advanced Study Princeton, New Jersey.
Entanglement Entropy from AdS/CFT Tadashi Takayanagi (Kyoto Univ.) Based on hep-th/ , , , , arXiv: , , ,
Utrecht University Gerard ’t Hooft and Isaac Newton Institute, December 15, 2004.
Higher spin AdS 3 holography and superstring theory Yasuaki Hikida (Rikkyo University) Based on collaborations with T. Creutzig (U. of Alberta) & P. B.
Strong coupling problems in condensed matter and the AdS/CFT correspondence HARVARD arXiv: Reviews: Talk online: sachdev.physics.harvard.edu arXiv:
알기 쉬운 초끈 이론 박 재모 (Postech). Outline 1. Partcle physics 2. Black holes 3. String theory 4. M theory 5. D branes 6. Gauge/Gravity theory correspondence.
Spectral function in Holographic superconductor Wen-Yu Wen (NTU) Taiwan String Theory Workshop 2010.
Heavy quark energy loss in finite length SYM plasma Cyrille Marquet Columbia University based on F. Dominguez, C. Marquet, A. Mueller, B. Wu and B.-W.
Quantum mechanics and the geometry of spacetime Juan Maldacena PPCM Conference May 2014.
Boundary conditions for SU(2) Yang-Mills on AdS 4 Jae-Hyuk Oh at 2012 workshop for string theory and cosmology, Pusan, Korea. Dileep P. Jatkar and Jae-Hyuk.
Gauge/gravity duality in Einstein-dilaton theory Chanyong Park Workshop on String theory and cosmology (Pusan, ) Ref. S. Kulkarni,
Condensed matter physics and string theory HARVARD Talk online: sachdev.physics.harvard.edu.
Rank-n logarithmic conformal field theory (LCFT) in the BTZ black hole Rank-n logarithmic conformal field theory (LCFT) in the BTZ black hole
Quantum Mechanical Models for Near Extremal Black Holes
Scale vs Conformal invariance from holographic approach
Toward a Holographic Model of d-wave Superconductors
NGB and their parameters
A rotating hairy BH in AdS_3
Exact Results in Massive N=2 Theories
Solutions of black hole interior, information paradox and the shape of singularities Haolin Lu.
On magnetization in holographic models
Based on the work submitted to EPJC
Hysteresis Curves from 11 dimensions
String Theory: A Status Report Institute for Advanced Study
Presentation transcript:

Friedel Oscillations and Horizon Charge in 1D Holographic Liquids Nabil Iqbal Kavli Institute for Theoretical Physics In collaboration with Thomas Faulkner:

Recently: a great deal of research trying to relate string theory to “condensed-matter” physics. Many results, but some basic questions remain unanswered. This talk will focus on one such question. ?

Compressible phases of quantum matter Consider a field theory with a conserved current J ρ ; turn on a chemical potential μ at T = 0. A compressible phase of matter: ρ(μ) is a continuously varying function of μ. How to do this? 1.Create a Fermi surface. 2.Or break a symmetry: if U(1), then superfluid; if translation, then solid. These are the only known possibilities (in “ordinary” field theory).

Weak coupling: Luttinger’s Theorem Conclude: a compressible phase that doesn’t break a symmetry has a Fermi surface. Example: free massive fermions in (1+1)d. Luttinger’s theorem: this relation holds to all orders in perturbation theory. How do we probe k F ?

Probing the Fermi Surface: Correlation functions:…or: Friedel oscillations Direct probe of underlying Fermi surface. Location fixed by Luttinger’s theorem.

Strong coupling: Holography A great deal of research (“AdS/CMT”) has discussed strongly coupled compressible phases arising from holography. + + Charged black hole horizon in the interior, e.g. Reissner-Nordstrom- AdS black hole. Very well-studied. In the field theory, what degrees of freedom carry this charge? Compressible, can be cooled to zero T -- Fermi surface? (Note: extensive study of fermions living outside the black hole (Lee; Liu, McGreevy, Vegh, Faulkner; Cubrovic, Zaanen, Shalm; etc.) ; these fermions are gauge-invariant and we will not discuss them here, because they already make sense).

Holographic Probes? (Edalati, Jottar, Leigh; Hartnoll, Shaghoulian) Can easily compute density-density correlation; linear response problem in AdS/CFT: No Friedel oscillations; indeed, no obvious structure in momentum space at all. This is a puzzle.

Why? Recall Luttinger’s theorem: If you were to take it seriously: Friedel oscillation location depends on q e, the charge of a single quantum excitation in the field theory. Black hole (and linearized perturbations) do not know about q e ; so they will miss this physics. Note however: bulk gauge symmetry is compact, so it does have a q e ; we need to include an ingredient that sees it.

1d Holographic Liquids From now on, specialize: study 2d field theory dual to compact Maxwell EM in AdS 3. Finite density state: charged BTZ black hole. (Theory is not quite conformal; logarithmic running, will break down in the UV and requires cutoff radius r Λ ) + +

Magnetic Monopoles If bulk gauge theory is compact, we can have magnetic monopoles in the bulk. Various ways to get them. We will not worry about where they come from: just assume they are very heavy: S m >> 1. + Localized instantons in 3d Euclidean spacetime. We will compute their effect on a holographic two-point function.

Working with monopoles To work with monopoles: dualize bulk photon, get a scalar. + Equation of motion: Monopoles are point sources:

Monopoles and Berry phases Note: this coupling means monopoles events feel a phase in a background field (analogous to Aharonov-Bohm phase) Thus, on the charged black hole each monopole knows where it is along the horizon.

Monopole corrections to correlators Usual AdS/CFT prescription: evaluate gravitational path integral via saddle point. Subleading saddles contribute via Witten diagrams:

Correlations between monopoles I Need to determine action cost of two well-separated monopoles. Depends on geometry. At high temperature: Effectively a 1d problem: Found Friedel oscillations from holography!

Correlations between monopoles II At zero temperature: monopole fields mix with gravity. Complicated. Charged BTZ black hole has a gapless sound mode, disperses with velocity v s. Creates long-range fields. Effectively a 2d problem: Found Friedel oscillations from holography (…at zero T)

Holographic Friedel Oscillations Found Friedel oscillations from holography. Results in rough agreement with existing field theory of interacting 1d liquids (Luttinger liquids); fine details disagree, probably due to lack of conformality.

Holography and Luttinger’s Theorem Location of singularity fixed by Berry phase: What is q m ? Take it to saturate bulk Dirac quantization condition: (expected in gravitational theory; see e.g. Banks, Seiberg). Precisely at the location predicted by Luttinger’s theorem. Note no fermions in sight.

Some thoughts (Any) 3d charged black hole has a Fermi surface! = ? We have found a Fermi momentum without fermions. Related to nonperturbative proofs of Luttinger’s theorem (Oshikawa, Yamanaka, Affleck). It is not clear whether we should associate this momentum with “the boundary of occupied single-particle states”. Note that in (1+1) dimensions we already have a robust field theory of interacting liquids. It would thus be fascinating to know if holographic mechanism extends to higher dimensions.

Summary Including nonperturbative effects, found Friedel oscillations in simple holographic model in one dimension. Indicate some robust structure in momentum space at momentum related to charge density by Luttinger’s theorem. Mechanism will work for any charged horizon in 3d. Perhaps a small step towards connecting AdS-described phases of matter with those of the real world. The End

Some other things…

Confinement in the bulk? Confinement in the bulk is dual to a charge gap in the boundary theory. In our model, the Berry phase tends to wipe out a coherent condensation of monopoles: no confinement. This is in agreement with cond-mat: no Mott insulators in one dimension unless explicit (commensurate) lattice. Suggests a way to holographically model insulating phases.

Relation to Chern-Simons Theory? Usually in 3d one considers Chern-Simons theories in the bulk. These are dual to 2d CFTs with a current algebra and so are rather constrained. However, Higgsing L-R with a scalar results in the Maxwell bulk theory described here (see e.g. Mukhi). Detailed connections remain to be worked out. In particular, monopoles in Chern-Simons theories are confined (Affleck et. al; Fradkin, Schaposnik).