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 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 Observables in inhomogeneous ground states at large global charge

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Simeon Hellerman ◽  
Nozomu Kobayashi ◽  
Shunsuke Maeda ◽  
Masataka Watanabe
Keyword(s):  
Ground State Energy ◽  
Ground State ◽  
State Energy ◽  
Point Function ◽  
Ground State Configuration ◽  
Charge Densities ◽  
Direct Extension ◽  
Fixed Set ◽  
State Configuration ◽  
Large Charge

Abstract As a sequel to previous work, we extend the study of the ground state configuration of the D = 3, Wilson-Fisher conformal O(4) model. In this work, we prove that for generic ratios of two charge densities, ρ1/ρ2, the ground-state configuration is inhomogeneous and that the inhomogeneity expresses itself towards longer spatial periods. This is the direct extension of the similar statements we previously made for ρ1/ρ2 ≪ 1. We also compute, at fixed set of charges, ρ1, ρ2, the ground state energy and the two-point function(s) associated with this inhomogeneous configuration on the torus. The ground state energy was found to scale (ρ1 + ρ2)3/2, as dictated by dimensional analysis and similarly to the case of the O(2) model. Unlike the case of the O(2) model, the ground also strongly violates cluster decomposition in the large-volume, fixed-density limit, with a two-point function that is negative definite at antipodal points of the torus at leading order at large charge.

MESONS AND DIQUARKS IN A NJL MODEL AT FINITE TEMPERATURE AND CHEMICAL POTENTIAL

1993 ◽  
Vol 08 (07) ◽  
pp. 1295-1312 ◽  
Author(s):  
D. EBERT ◽  
YU. L. KALINOVSKY ◽  
L. MÜNCHOW ◽  
M.K. VOLKOV
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Finite Temperature ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Baryon Number ◽  
Coupling Constants ◽  
Number Density ◽  
Njl Model

An extended NJL model with [Formula: see text] and (qq)-interactions is studied at finite temperature and baryon number density. We investigate the chiral symmetry breaking, its restoration and the behavior of meson and diquark masses, decay and coupling constants as functions of T and µ.

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.

STANDING WAVE GROUND STATE IN HIGH DENSITY, ZERO TEMPERATURE QCD AT LARGE NC

1992 ◽  
Vol 07 (04) ◽  
pp. 659-681 ◽  
Author(s):  
D. V. DERYAGIN ◽  
D. YU. GRIGORIEV ◽  
V. A. RUBAKOV
Keyword(s):  
Symmetry Breaking ◽  
Standing Wave ◽  
Ground State ◽  
Chemical Potential ◽  
Chiral Symmetry Breaking ◽  
Mass Operator ◽  
Ladder Approximation ◽  
Zero Temperature ◽  
Density Zero ◽  
Bilocal Field

Chiral symmetry breaking in QCD at zero temperature and high fermionic density is studied in the limit NC → ∞. We evaluate the effective action in the ladder approximation and integrate out fermions by introducing the bilocal field Σ(x, y), which enters the action as the mass operator for fermions. It is argued that at large fermionic chemical potential the mass operator Σ(x, y) has a small but nonvanishing expectation value. The condensate of the field Σ(x, y) and the fermionic condensate [Formula: see text] are inhomogeneous and anisotropic, so that the ground state has the structure of the standing wave with respect to these order parameters. Unlike possible color superconductivity, this symmetry breaking occurs to the leading order in 1/NC.

scholarly journals Cascade of phase transitions in a planar Dirac material

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Takuya Kanazawa ◽  
Mario Kieburg ◽  
Jacobus J.M. Verbaarschot
Keyword(s):  
Phase Diagram ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
Ground State ◽  
Chemical Potential ◽  
Three Dimensional ◽  
Dirac Fermions ◽  
First Order ◽  
First Order Phase ◽  
Parity Breaking

Abstract We investigate a model of interacting Dirac fermions in 2 + 1 dimensions with M flavors and N colors having the U(M)×SU(N ) symmetry. In the large-N limit, we find that the U(M) symmetry is spontaneously broken in a variety of ways. In the vacuum, when the parity-breaking flavor-singlet mass is varied, the ground state undergoes a sequence of M first-order phase transitions, experiencing M + 1 phases characterized by symmetry breaking U(M)→U(M − k)×U(k) with k ∈ {0, 1, 2, · · · , M}, bearing a close resemblance to the vacuum structure of three-dimensional QCD. At finite temperature and chemical potential, a rich phase diagram with first and second-order phase transitions and tricritical points is observed. Also exotic phases with spontaneous symmetry breaking of the form as U(3)→U(1)3, U(4)→U(2)×U(1)2, and U(5)→U(2)2×U(1) exist. For a large flavor-singlet mass, the increase of the chemical potential μ brings about M consecutive first-order transitions that separate the low-μ phase diagram with vanishing fermion density from the high-μ region with a high fermion density.

scholarly journals More on complex Sachdev-Ye-Kitaev eternal wormholes

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pengfei Zhang
Keyword(s):  
Black Hole ◽  
Ground State ◽  
Effective Action ◽  
Chemical Potential ◽  
Specific Charge ◽  
Zero Temperature ◽  
Small Coupling ◽  
Chemical Potentials ◽  
Quench Dynamics ◽  
Two Sides

Abstract In this work, we study a generalization of the coupled Sachdev-Ye-Kitaev (SYK) model with U(1) charge conservations. The model contains two copies of the complex SYK model at different chemical potentials, coupled by a direct hopping term. In the zero-temperature and small coupling limit with small averaged chemical potential, the ground state is an eternal wormhole connecting two sides, with a specific charge Q = 0, which is equivalent to a thermofield double state. We derive the conformal Green’s functions and determine corresponding IR parameters. At higher chemical potential, the system transit into the black hole phase. We further derive the Schwarzian effective action and study its quench dynamics. Finally, we compare numerical results with the analytical predictions.

scholarly journals Symmetry breaking at high temperatures in large N gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Soumyadeep Chaudhuri ◽  
Eliezer Rabinovici
Keyword(s):  
Fixed Point ◽  
Phase Transitions ◽  
Symmetry Breaking ◽  
High Temperatures ◽  
Gauge Theories ◽  
Scalar Fields ◽  
Temperature Limit ◽  
Spontaneous Breaking ◽  
Critical Temperatures ◽  
Weakly Coupled

Abstract Considering marginally relevant and relevant deformations of the weakly coupled (3 + 1)-dimensional large N conformal gauge theories introduced in [1], we study the patterns of phase transitions in these systems that lead to a symmetry-broken phase in the high temperature limit. These deformations involve only the scalar fields in the models. The marginally relevant deformations are obtained by varying certain double trace quartic couplings between the scalar fields. The relevant deformations, on the other hand, are obtained by adding masses to the scalar fields while keeping all the couplings frozen at their fixed point values. At the N → ∞ limit, the RG flows triggered by these deformations approach the aforementioned weakly coupled CFTs in the UV regime. These UV fixed points lie on a conformal manifold with the shape of a circle in the space of couplings. As shown in [1], in certain parameter regimes a subset of points on this manifold exhibits thermal order characterized by the spontaneous breaking of a global ℤ2 or U(1) symmetry and Higgsing of a subset of gauge bosons at all nonzero temperatures. We show that the RG flows triggered by the marginally relevant deformations lead to a weakly coupled IR fixed point which lacks the thermal order. Thus, the systems defined by these RG flows undergo a transition from a disordered phase at low temperatures to an ordered phase at high temperatures. This provides examples of both inverse symmetry breaking and symmetry nonrestoration. For the relevant deformations, we demonstrate that a variety of phase transitions are possible depending on the signs and magnitudes of the squares of the masses added to the scalar fields. Using thermal perturbation theory, we derive the approximate values of the critical temperatures for all these phase transitions. All the results are obtained at the N → ∞ limit. Most of them are found in a reliable weak coupling regime and for others we present qualitative arguments.

scholarly journals Quark Number Susceptibilities and Equation of State in QCD at Finite μB

Proceedings ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 5
Author(s):  
Saumen Datta ◽  
Rajiv Gavai ◽  
Sourendu Gupta
Keyword(s):  
Equation Of State ◽  
Taylor Series ◽  
Chemical Potential ◽  
Baryon Number ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collider ◽  
Quark Number ◽  
Monte Carlo Studies ◽  
Essential Input ◽  
Beam Energy Scan

One of the main goals of the cold baryonic matter (CBM) experiment at FAIR is to explore the phases of strongly interacting matter at finite temperature and baryon chemical potential μ B . The equation of state of quantum chromodynamics (QCD) at μ B > 0 is an essential input for the CBM experiment, as well as for the beam energy scan in the Relativistic Heavy Ion Collider(RHIC) experiment. Unfortunately, it is highly nontrivial to calculate the equation of state directly from QCD: numerical Monte Carlo studies on lattice are not useful at finite μ B . Using the method of Taylor expansion in chemical potential, we estimate the equation of state, namely the baryon number density and its contribution to the pressure, for two-flavor QCD at moderate μ B . We also study the quark number susceptibilities. We examine the technicalities associated with summing the Taylor series, and explore a Pade resummation. An examination of the Taylor series can be used to get an estimate of the location of the critical point in μ B , T plane.

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