Unravelling the novel Higgs mechanism in (2+1)d Chern-Simons theories
TL;DR: In this paper, a non-propagating Chern-Simons field acquiring a massless propagating mode via a Higgs mechanism was studied without reference to M-theory or supersymmetry.
Abstract: Chern-Simons gauge theories in 2+1 dimensions with multiple gauge fields exhibit novel properties that are analysed here in some detail. A striking feature is the possibility of a non-propagating Chern-Simons field acquiring a massless propagating mode via a Higgs mechanism. This novel Higgs mechanism, originally discovered in the context of M-theory, is studied here without reference to M-theory or supersymmetry. It is revealed as a variant of topological mass generation and shown to arise only when Chern-Simons and mass matrices are not simultaneously diagonalisable. Sufficient conditions are found for it to occur. It is speculated that some analogue of the NHM could occur in theories of condensed-matter systems similar to those exhibiting the fractional quantum Hall effect, as well as in 2+1 dimensional gravity.
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TL;DR: In this article, the authors review developments in the theory of multiple, parallel membranes in M-theory and introduce 3-algebras, leading to distinct classes of 2+1 dimensional theories with varying degrees of supersymmetry.
129 citations
TL;DR: In this article, the existence of Friedel oscillations in a 3D gravity dual to a compressible finite-density state in a (1+1) dimensional field theory was demonstrated.
Abstract: In many-body fermionic systems at finite density correlation functions of the density operator exhibit Friedel oscillations at a wavevector that is twice the Fermi momentum. We demonstrate the existence of such Friedel oscillations in a 3d gravity dual to a compressible finite-density state in a (1+1) dimensional field theory. The bulk dynamics is provided by a Maxwell U(1) gauge theory and all the charge is behind a bulk horizon. The bulk gauge theory is compact and so there exist magnetic monopole tunneling events. We compute the effect of these monopoles on holographic density-density correlation functions and demonstrate that they cause Friedel oscillations at a wavevector that directly counts the charge behind the bulk horizon. If the magnetic monopoles are taken to saturate the bulk Dirac quantization condition then the observed Fermi momentum exactly agrees with that predicted by Luttinger’s theorem, suggesting some Fermi surface structure associated with the charged horizon. The mechanism is generic and will apply to any charged horizon in three dimensions. Along the way we clarify some aspects of the holographic interpretation of Maxwell electromagnetism in three bulk dimensions and show that perturbations about the charged BTZ black hole exhibit a hydrodynamic sound mode at low temperature.
60 citations
TL;DR: In this paper, the anomalous dimension of the primary operator of a Chern-Simons theory coupled to fermions was studied in the limit M ≪ N, where k = 1 and N is large.
Abstract: Non-abelian Chern-Simons theories coupled to fermions are known to provide an interesting class of non-supersymmetric conformal fixed points [1]. These theories, particularly those based on bifundamental matter, are important because they may provide simple non-supersymmetric examples of the AdS/CFT correspondence. For instance, it seems natural to conjecture that O(N)−k
× O(N)
k
Chern-Simons theory coupled to Majorana fermions transforming in a bi-vector representation may be dual to pure Einstein gravity with a small negative cosmological constant in the “M-theory” limit where k = 1 and N is large. While it is extremely difficult to directly study such bifundamental theories when k = 1 or even at strong ’t Hooft coupling $$ \lambda =\frac{N}{k} $$
, it is possible to calculate physical quantities to all orders in λ in a $$ \mathrm{U}{(M)}_{k_M}\times \mathrm{U}{(N)}_{k_N} $$
theory, in the limit M ≪ N, in an M/N expansion. To illustrate this, we calculate the anomalous dimension of the primary operator tr $$ \overline{\psi}\psi $$
, to first order in M/N, to all orders in $$ {\lambda}_M=\frac{N}{k_M} $$
, but with $$ {\lambda}_N=\frac{N}{k_N} = 0 $$
. We also comment on possible bosonization dualities for bifundamental Chern-Simons theories.
45 citations
TL;DR: In this article, the authors presented the first analytic analysis of the six-point two-loop amplitude of ABJM theory and showed that the two-layer amplitude consists of corrections proportional to two distinct local Yangian invariants, which can be identified as the tree-and one-loop amplitudes respectively.
Abstract: In this paper we present the first analytic computation of the six-point two-loop amplitude of ABJM theory. We show that the two-loop amplitude consists of corrections proportional to two distinct local Yangian invariants which can be identified as the tree- and the one-loop amplitude respectively. The two-loop correction proportional to the tree-amplitude is identical to the one-loop BDS result of $ \mathcal{N}=4 $
SYM plus an additional remainder function, while the correction proportional to the one-loop amplitude is finite. Both the remainder and the finite correction are dual conformal invariant, which implies that the two-loop dual conformal anomaly equation for ABJM is again identical to that of one-loop $ \mathcal{N}=4 $
super Yang-Mills, as was first observed at four-point. We discuss the theory on the Higgs branch, showing that its amplitudes are infrared finite, but equal, in the small mass limit, to those obtained in dimensional regularization.
41 citations
TL;DR: In this paper, the authors discuss some special background solutions that arise in topological gauged N = 8$ three-dimensional CFTs with SO(N) gauge group and discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in various backgrounds and argue that some properties are due to their common origin in a conformal phase.
Abstract: In this paper we discuss some special (critical) background solutions that arise in topological gauged ${\mathcal N}=8$ three-dimensional CFTs with SO(N) gauge group. These solutions solve the TMG equations (containing the parameters $\mu$ and $l$) for a certain set of values of $\mu l$ obtained by varying the number of scalar fields with a VEV. Apart from Minkowski, chiral round $AdS_3$ and null-warped $AdS_3$ (or Schr\"odinger(z=2)) we identify also a more exotic solution recently found in $TMG$ by Ertl, Grumiller and Johansson. We also discuss the spectrum, symmetry breaking pattern and the supermultiplet structure in the various backgrounds and argue that some properties are due to their common origin in a conformal phase. Some of the scalar fields, including all higgsed ones, turn out to satisfy three-dimensional singleton field equations. Finally, we note that topologically gauged ${\mathcal N}=6$ ABJ(M) theories have a similar, but more restricted, set of background solutions.
22 citations
References
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Book•
19 May 2003TL;DR: A survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources can be found in this paper, where the solutions are ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties.
Abstract: A paperback edition of a classic text, this book gives a unique survey of the known solutions of Einstein's field equations for vacuum, Einstein-Maxwell, pure radiation and perfect fluid sources. It introduces the foundations of differential geometry and Riemannian geometry and the methods used to characterize, find or construct solutions. The solutions are then considered, ordered by their symmetry group, their algebraic structure (Petrov type) or other invariant properties such as special subspaces or tensor fields and embedding properties. Includes all the developments in the field since the first edition and contains six completely new chapters, covering topics including generation methods and their application, colliding waves, classification of metrics by invariants and treatments of homothetic motions. This book is an important resource for graduates and researchers in relativity, theoretical physics, astrophysics and mathematics. It can also be used as an introductory text on some mathematical aspects of general relativity.
3,502 citations
TL;DR: In this paper, the authors constructed three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(n) and SU(N), SU(2) × SU (2) which have explicit = 6 superconformal symmetry.
Abstract: We construct three dimensional Chern-Simons-matter theories with gauge groups U(N) × U(N) and SU(N) × SU(N) which have explicit = 6 superconformal symmetry. Using brane constructions we argue that the U(N) × U(N) theory at level k describes the low energy limit of N M2-branes probing a C4/Zk singularity. At large N the theory is then dual to M-theory on AdS4 × S7/Zk. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS4 × CP3. For k = 1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d = 3 gauge theories. When the gauge group is SU(2) × SU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.
3,091 citations
TL;DR: By disentangling the hamiltonian constraint equations, 2 + 1 dimensional gravity (with or without a cosmological constant) is shown to be exactly soluble at the classical and quantum levels.
2,636 citations
TL;DR: It is proposed that the fractional quantum Hall effect of electrons can be physically understood as a manifestation of the integer quantumHall effect of composite fermionic objects consisting of electrons bound to an even number of flux quanta.
Abstract: In the standard hierarchical scheme the daughter state at each step results from the fractional quantum Hall effect of the quasiparticles of the parent state. In this paper a new possible approach for understanding the fractional quantum Hall effect is presented. It is proposed that the fractional quantum Hall effect of electrons can be physically understood as a manifestation of the integer quantum Hall effect of composite fermionic objects consisting of electrons bound to an even number of flux quanta.
1,625 citations