scholarly journals Large charge sector of 3d parity-violating CFTs

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Gabriel Cuomo ◽  
Luca V. Delacrétaz ◽  
Umang Mehta
Keyword(s):  
Effective Field Theory ◽  
Ground State ◽  
Chemical Potential ◽  
Effective Field ◽  
Weakly Coupled ◽  
Matter Theory ◽  
Derivative Term ◽  
Chern Simons ◽  
Charge Sector ◽  
Large Charge

Abstract Certain CFTs with a global U(1) symmetry become superfluids when coupled to a chemical potential. When this happens, a Goldstone effective field theory controls the spectrum and correlators of the lightest large charge operators. We show that in 3d, this EFT contains a single parity-violating 1-derivative term with quantized coefficient. This term forces the superfluid ground state to have vortices on the sphere, leading to a spectrum of large charge operators that is remarkably richer than in parity-invariant CFTs. We test our predictions in a weakly coupled Chern-Simons matter theory.

scholarly journals Gapped Goldstones at the cut-off scale: a non-relativistic EFT

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
G. Cuomo ◽  
A. Esposito ◽  
E. Gendy ◽  
A. Khmelnitsky ◽  
A. Monin ◽  
...  
Keyword(s):  
Effective Field Theory ◽  
Chemical Potential ◽  
Effective Field ◽  
Energy Scale ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Charge Sector ◽  
Large Charge

Abstract At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU(2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries.

scholarly journals Chern-Simons-matter theories at large baryon number

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Masataka Watanabe
Keyword(s):  
Fixed Point ◽  
Quantitative Analysis ◽  
Symmetry Breaking ◽  
Ground State ◽  
Chemical Potential ◽  
Baryon Number ◽  
Classical Analysis ◽  
Chern Simons ◽  
State Configuration ◽  
Large Charge

Abstract We study SU(2) Chern-Simons theories at level k coupled to a scalar on T2 × ℝ at large baryon number. We find a homogeneous but anisotropic ground state configuration for any values of k on the IR fixed-point of those models. This classical analysis is valid as long as we take the baryon number large. As a corollary, by comparing the symmetry breaking pattern at large chemical potential, we find that the theory does not reduce to the singlet sector of the O(4) Wilson-Fisher fixed-point at large-k, as expected from general grounds. This paper will be one primitive step towards quantitative analysis of Chern-Simons-matter dualities using the large charge expansion.

scholarly journals Extremal correlators and random matrix theory

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Alba Grassi ◽  
Zohar Komargodski ◽  
Luigi Tizzano
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Matrix Model ◽  
Effective Field Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Matrix Theory ◽  
Effective Field ◽  
Random Matrix Model ◽  
Large Charge

Abstract We study the correlation functions of Coulomb branch operators of four-dimensional $$ \mathcal{N} $$ N = 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.

scholarly journals A Chern-Simons effective field theory for the Pfaffian quantum Hall state

1998 ◽  
Vol 516 (3) ◽  
pp. 704-718 ◽  
Author(s):  
Eduardo Fradkin ◽  
Chetan Nayak ◽  
Alexei Tsvelik ◽  
Frank Wilczek
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Quantum Hall ◽  
Effective Field ◽  
Chern Simons ◽  
Quantum Hall State

scholarly journals Properties of infrared extrapolations in a harmonic oscillator basis

2016 ◽  
Vol 25 (05) ◽  
pp. 1641011 ◽  
Author(s):  
Sidney A. Coon ◽  
Michael K. G. Kruse
Keyword(s):  
Effective Field Theory ◽  
Ground State ◽  
Effective Field ◽  
The Other ◽  
Ab Initio Methods ◽  
Harmonic Oscillator Basis ◽  
Expectation Values ◽  
Oscillator Basis ◽  
Model Spaces ◽  
Ground State Energies

The success and utility of effective field theory (EFT) in explaining the structure and reactions of few-nucleon systems has prompted the initiation of EFT-inspired extrapolations to larger model spaces in ab initio methods such as the no-core shell model (NCSM). In this contribution, we review and continue our studies of infrared (ir) and ultraviolet (uv) regulators of NCSM calculations in which the input is phenomenological [Formula: see text] and [Formula: see text] interactions fitted to data. We extend our previous findings that an extrapolation in the ir cutoff with the uv cutoff above the intrinsic uv scale of the interaction is quite successful, not only for the eigenstates of the Hamiltonian but also for expectation values of operators, such as [Formula: see text], considered long range. The latter results are obtained with Hamiltonians transformed by the similarity renormalization group (SRG) evolution. On the other hand, a possible extrapolation of ground state energies in the uv cutoff when the ir cutoff is below the intrinsic ir scale is not robust and does not agree with the ir extrapolation of the same data or with independent calculations using other methods.

scholarly journals Matter in 2+1 Dimensions at Finite Density with Chern Simons Interactions

2020 ◽  
Author(s):  
◽  
Stanislav Stratiev
Keyword(s):  
Ground State ◽  
Particle Number ◽  
Chemical Potential ◽  
Vacuum Expectation ◽  
Simons Theory ◽  
Vortex Solutions ◽  
Scalar Potentials ◽  
Chern Simons ◽  
Do So ◽  
Chern Simons Theory

We study several matter Chern-Simons models at finite chemical potential. In the SU(N) theory we discover a colour-flavour locked Bose condensed ground state with vacuum expectation values for both the scalar and gauge fields. We identify this ground state with the non-commutative Chern-Simons description of the quan-tum Hall eect. We compute the quadratic spectrum and discover roton excitations. We find a self-consistent circularly symmetric ansatz for topological non-abelian vortices. We examine vortices in abelian Chern-Simons theory coupled to a relativistic scalar field with a chemical potential for particle number or U(1) charge. The Gauss constraint requires chemical potential for the local symme-try to be accompanied by a constant background charge density/ma-gnetic field. Focusing attention on power law scalar potentials |Φ|2s, s ∈ Z, which do not support vortex configurations in vacuum but do so at finite chemical potential, we numerically study classical vortex solutions for a large winding number |n|  1.

scholarly journals Massive Nambu–Goldstone fermions and bosons for non-relativistic superconformal symmetry: Jackiw–Pi vortices in a trap

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Toshiaki Fujimori ◽  
Muneto Nitta ◽  
Keisuke Ohashi
Keyword(s):  
Chemical Potential ◽  
Rotation Velocity ◽  
Supersymmetric Extension ◽  
Superconformal Symmetry ◽  
Fermion Number ◽  
Relativistic Version ◽  
Matter Theory ◽  
Bps States ◽  
Chern Simons ◽  
Goldstone Modes

Abstract We discuss a supersymmetric extension of a non-relativistic Chern–Simons matter theory, known as the supersymmetric Jackiw–Pi model, in a harmonic trap. We show that the non-relativistic version of the superconformal symmetry, called the super-Schrödinger symmetry, is not spoiled by an external field including the harmonic potential. It survives as a modified symmetry whose generators have explicit time dependences determined by the strength of the trap, the rotation velocity of the system, and the fermion number chemical potential. We construct 1/3 Bogomol'nyi–Prasad–Sommerfield (BPS) states of trapped Jackiw–Pi vortices preserving part of the modified superconformal symmetry and discuss fluctuations around static BPS configurations. In addition to the bosonic massive Nambu–Goldstone modes, we find that there exist massive Nambu–Goldstone fermions associated with broken generators of the modified super-Schrödinger symmetry. Furthermore, we find that eigenmodes form supermultiplets of a modified supersymmetry preserved by the static BPS backgrounds. As a consequence of the modified supersymmetry, infinite towers of explicit spectra can be found for eigenmodes corresponding to bosonic and fermionic lowest Landau levels.

Sign in / Sign up

Export Citation Format

Share Document