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Trace anomaly form factors from lattice QCD
The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to Q 2 ∼ 4.3 GeV 2 and the nucleon up to Q 2 ∼ 1 GeV 2 . The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from ∼ 250 to ∼ 540 MeV , including the unitary point ∼ 340 MeV . We calculate the radius of the glue trace anomaly for the pion and the nucleon from the z expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society 2024
Non-conformal attractor in boost-invariant plasmas
We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they approach the hydrodynamic limit only late, at small values of the inverse Reynolds numbers. Only the longitudinal pressure, which is a combination of thermal, shear and bulk viscous pressures, continues to show early approach to a far-off-equilibrium attractor, driven by the rapid longitudinal expansion at early times. Second-order dissipative hydrodynamics based on a gradient expansion around locally isotropic thermal equilibrium fails to reproduce this attractor.
Cosmological quasiparticles and the cosmological collider
The interplay between cosmology and strongly coupled dynamics can yield transient spectral features that vanish at late times, but which may leave behind phenomenological signatures in the spectrum of primordial fluctuations. Of particular interest are strongly coupled extensions of the standard model featuring approximate conformal invariance. In flat space, the spectral density for a scalar operator in a conformal field theory is characterized by a continuum with scaling law governed by the dimension of the operator, and is otherwise featureless. Anti–de Sitter/conformal field theory arguments suggest that for large 𝑁, in an inflationary background with Hubble rate 𝐻, this continuum is gapped. We demonstrate that there can be additional peak structures that become sharp and particlelike at phenomenologically interesting regions in parameter space, and we estimate their contribution to cosmological observables. We find phenomena that are potentially observable in future experiments that are unique to these models, including displaced oscillatory features in the squeezed limit of the bispectrum. These particles can be either fundamental, and localized to a UV brane, or composite at the Hubble scale, 𝐻, and bound to a horizon in the bulk of the 5D geometry. We comment on how stabilization of conformal symmetry breaking vacua can be correlated with these spectral features and their phenomenology.
Novel features of attractors and transseries in nonconformal Bjorken flows
In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the nonconformal hydrodynamic equations of a longitudinal boost invariant expanding plasma. The new transseries solutions unveil a rich physical structure which arises due to the interplay of different physical scales. In the perfect fluid case the nonconformal speed of sound slows down the cooling of the temperature due to the emergence of logarithmic corrections that depends on the mass of the particle. Further, these terms propagate into the perturbative and nonperturbative sectors of the transseries once viscous corrections are included. The logarithmic mass contributions increase the asymptotic value of the Knudsen number while decreasing the damping rate of the transient nonhydrodynamic modes and thus, yielding to an extremely slow hydrodynamization process where flow lines merge to their forward attractor at extremely late times. The early time free streaming expansion is modified and receives logarithmic mass corrections induced by the shear-bulk couplings. The global flow structure and numerical analyses carried out in our work demonstrate the existence of local attraction at early and late times for the shear viscous tensor and bulk viscous pressure.
Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum
We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji′s invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.
Quantum Critical Higgs: from AdS 5 to colliders
We examine distinctive signatures of Quantum Critical Higgs models at the LHC and future higher energy colliders. In these models the Higgs boson is part of a conformal sector that is softly broken at a threshold scale, and generically the scaling dimension of the Higgs is larger than in the Standard Model. In particular we examine the gg → H → ZZ, gg → H → γγ, and gg → Z → H Z channels to see how the cross sections deviate from the Standard Model in the high invariant mass region. In order to perform the calculations we use 5D duals of Quantum Critical Higgs models using the AdS/CFT correspondence, with a soft wall to break the conformal symmetry.
Hadrons, superconductor vortices, and cosmological constant
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Pion gravitational form factors in the QCD instanton vacuum. I
The pion form factors of the QCD energy-momentum tensor (EMT) are studied in the instanton liquid model (ILM) of the QCD vacuum. In this approach, the breaking of conformal symmetry is encoded in the form of stronger-than-Poisson fluctuations in the number of instantons. For the trace of the EMT, it is shown that the gluonic trace anomaly term contributes half the pion mass, with the other half coming from the quark-mass-dependent σ term. The Q 2 dependence of the form factors is governed by glueball and scalar meson exchanges. For the EMT, the spin-0 (trace) and spin-2 (traceless rank-2 tensor) form factors are computed at next-to-leading order in the instanton density using effective quark operators. Relations between the gluon and quark contributions to the EMT form factors are derived. The form factors are also expressed in terms of the pion light-front wave functions in the ILM. The results at the low resolution scale of the inverse instanton size are evolved to higher scales using the renormalization group equation. The ILM results compare well with those of recent lattice QCD calculations. Published by the American Physical Society 2024
Can black holes preserve 𝒩 > 4 supersymmetry?
The dynamics of near-BPS black holes are governed by the breaking of the conformal symmetry that emerges near their horizons. Using the classification of superconformal symmetries, we systematically classify and quantize all effective theories that can arise in the near-BPS limit of black holes. Using these results, we argue — under certain physical assumptions — that BPS black holes cannot preserve more than four supercharges. This conclusion is consistent with existing constructions in string theory.
Spontaneous breaking of finite group symmetries at all temperatures
We study conformal field theories with finite group symmetries with spontaneous symmetry breaking (SSB) phases which persist at all temperatures. We work with two \lambda \phi^4 λ ϕ 4 theories coupled through their mass terms. The two \lambda \phi^4 λ ϕ 4 theories are chosen to preserve either the cubic symmetry group, or the tetrahedral symmetry group. A one-loop calculation in the 4-\epsilon 4 − ϵ expansion shows that there exist infinitely many fixed points that can host an all temperature SSB phase. An analysis of the renormalization group (RG) stability matrix of these fixed points, reveals that their spectrum contains at least three relevant operators. In other words, these fixed points are tetracritical points.
AdS Higgs mechanism from double trace deformed CFT
Explicit breaking of a global symmetry in a conformal field theory is holographically dual to giving mass to a gauge field living in AdS via the Higgs mechanism. We show that if this breaking is induced via a double trace deformation the Higgs mechanism is induced via a scalar loop diagram. The mass can be calculated analytically in both bulk and field theory and we find perfect agreement. While representing familiar physics, the mechanism is identical to how the graviton picks up a mass in the holographic dual of a conformal field theory coupled to a bath.
Entanglement asymmetry and symmetry defects in boundary conformal field theory
A state in a quantum system with a given global symmetry, G, can be sensitive to the presence of boundaries, which may either preserve or break this symmetry. In this work, we investigate how conformal invariant boundary conditions influence the G-symmetry breaking through the lens of the entanglement asymmetry, a quantifier of the “distance” between a symmetry-broken state and its symmetrized counterpart. By leveraging 2D boundary conformal field theory (BCFT), we investigate the symmetry breaking for both finite and compact Lie groups. Beyond the leading order term, we also compute the subleading corrections in the subsystem size, highlighting their dependence on the symmetry group G and the BCFT operator content. We further explore the entanglement asymmetry following a global quantum quench, where a symmetry-broken state evolves under a symmetry-restoring Hamiltonian. In this dynamical setting, we compute the entanglement asymmetry by extending the method of images to a BCFT with non-local objects such as invertible symmetry defects.
Mass-induced confinement near the sill of the conformal window
We revisit standard arguments for hyperscaling of the spectrum when a nonzero fermion mass is introduced to a gauge-fermion theory which is conformal in the infrared limit. With some general assumptions, we argue that the induced confinement scale will be significantly enhanced near the edge of the conformal to confining transition. This enhancement can allow for the fermion mass to be arbitrarily small compared to the confinement scale. This scale separation may allow for apparent spontaneous breaking of chiral symmetry within the conformal window, which may be of interest for construction of dilaton effective field theories in this regime.
Broken conformal window
We show that near the edges of the conformal window of supersymmetric SU(Nc) QCD, perturbed by Anomaly Mediated Supersymmetry Breaking (AMSB), chiral symmetry can be broken depending on the initial conditions of the RG flow. We do so by perturbatively expanding around Banks-Zaks fixed points and taking advantage of Seiberg duality. Interpolating between the edges of the conformal window, we predict that non-supersymmetric QCD breaks chiral symmetry up to N f ≤ 3N c − 1, while we cannot say anything definitive for N f ≥ 3N c at this moment.
Hidden conformal symmetry from the lattice
We analyze newly expanded and refined data from lattice studies of an SU(3) gauge theory with eight Dirac fermions in the fundamental representation. We focus on the light composite states emerging from these studies, consisting of a set of pseudoscalars and a single light scalar. We first consider the view that this theory is just outside the conformal window. In this case, the pseudoscalars arise from spontaneous breaking of chiral symmetry. Identifying the scalar in this case as an approximate dilaton, we fit the lattice data to a dilaton effective field theory, finding that it yields a good fit even at lowest order. For comparison, we then consider the possibility that the theory is inside the conformal window. The fermion mass provides a deformation, triggering confinement. We employ simple scaling laws to fit the lattice data, and find that it is of lesser quality.
a -anomalous interactions of the holographic dilaton
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Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
The study of fermionic quantum field theories is an important problem for realizing the standard model of particle physics on a quantum computer. As a step towards this goal, we consider the massive Thirring and Gross--Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$ in the Hamiltonian formulation. We compute the gate complexity using the higher-order product formula and using block-encoding/qubitization and quantum singular value transformations in the limit of large $N_f$ and $L$. We also prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$ using the adaptive-variational quantum imaginary time algorithm. In addition, we also classify the dynamical Lie algebras of these relativistic fermionic models and show that they belong to the same isomorphism class. Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models relevant for chiral symmetry breaking, understanding dimensional transmutation, and exploring the conformal window of field theories on near-term and early fault-tolerant quantum computers.