I examine the phenomena of the chromomagnetic gluon condensation in the Yang-Mills theory and the problem of stability of the chromomagnetic vacuum fields. The apparent instability of the chromomagnetic vacuum fields is a result of quadratic approximation. The stability is restored when the nonlinear interaction of negative/unstable modes is taken into account in the case of chromomagnetic vacuum fields and the interaction of the zero modes in the case of (anti)self-dual covariantly-constant vacuum fields. All these vacuum fields are stable and indicate that the Yang-Mills vacuum is highly degenerate quantum state.
A key objective of nuclear physics is mapping out the phase diagram of QCD in the baryon density-temperature plane. Several major collider experiments are probing this question, and a simultaneous effort is targeting QCD phase structure from first principles. However, these efforts have been stymied by a lattice sign problem associated with a complex fermion determinant and non-Hermitian transfer matrix. Fortunately, finite-density QCD is also invariant under CK symmetry, or combined charge and complex conjugation invariance. CK belongs to the class of PT-type symmetries, which are widely studied in optics and condensed matter for their unique properties. We discuss recently developed analytic and numerical methods for field theories with non-Hermitian transfer matrices and PT-type symmetries, including techniques to overcome sign problems. We demonstrate that such theories generally support exotic behaviors including inhomogeneous phases, Friedel-oscillatory phases, and disorder lines near a second-order critical point. We analyze the appearance of these exotic phases in a number of simple models of dense QCD using analytics and lattice simulation, and we discuss potential observables for exotic phases at RHIC. Finally, we make the case that a deeper fundamental understanding of non-Hermitian and PT-symmetric field theories is key to accelerating progress on finite-density QCD.
In the talk I will present some selected recent results on
the phases of (strongly) interacting relativistic Fermi systems
in lower dimensions. These include Gross-Neveu and Thirring
type models, the breaking of their symmetries and the presence or
absence of inhomogeneous condensates.
Quantum many-body systems present us with intractable optimization problems, e.g. finding the ground state of a many-body system. This problem is most often addressed through the variational ansatz approach, where physical insight can guide us in constructing the correct ansatz for a given system. Yet, variational methods can only provide us with a one sided estimate---an upper bound on the ground state energy. To certify a variational solution a lower bound is also required. Lower bounds can be obtained through so-called relaxation methods. In this approach the optimization problem is simplified by omitting (relaxing) some of the constraints that define the set of admissible optimization variables. (The name relaxation refers to relaxing constraints---not to be confused with any physical relaxation process.) This approach can be applied in the many-body setting if instead of minimizing the energy with respect to global quantum states, one has the local reduced density matrix as the optimization variable. The admissible (i.e. physical) reduced density matrices are those which are compatible with a global state. Relaxing this constraint leads to lower bounds on the ground state energy. Relaxation methods have been applied to many-body systems since the 50s and have also proven to be an essential tool in tackling various problems in quantum information theory and conformal field theory (the numerical bootstrap). Such methods, however, suffer from the drawback of exponential scaling of their complexity with the accuracy of the solution. In contrast, variational algorithms such as the density matrix renormalization group (DMRG), and other tensor-network algorithms which are based on the renormalization group idea, exhibit polynomial scaling. In this talk I will describe how one can incorporate the power of the renormalization group approach into the relaxation framework to efficiently compute lower bounds. I will present the results we obtained with this method for translation-invariant spin chains where we observe a polynomial scaling of the complexity with the accuracy.
We describe a new method for computing Feynman integrals based on solving inequality constraints, inspired by work on bootstrapping quantum mechanics and lattice models. The starting point is that a convergent Euclidean integral is non-negative if its integrand is non-negative. Combined with integration-by-parts reduction, this places powerful constraints on the values of master integrals, which can be solved efficiently using the numerical technique of semidefinite programming. We also find hidden consistency relations between terms at different orders in $\epsilon$ in dimensional regularization. We present examples with up to three loops.
Relativistic hydrodynamics has emerged as an important topic of 21st century research due applications to ultrarelativistic nuclear collisions, connections with holographic black hole physics and now also description of neutron star mergers. Our contemporary understanding of this topic is based on the principle of an effective field theory, in which case the only information not obviously constrained by symmetries is hidden in transport coefficients such as shear viscosity. To date, a significant effort has been made to explicitly compute transport coefficients in various microscopic models. I will present a different approach in which one is not directly interested in the value of a particular transport coefficient in a given theory, but rather in what ranges of values are allowed by relativistic causality in any sensible theory. This new way of thinking about relativistic hydrodynamics, close in some sense to philosophy behind the KSS bound but otherwise mathematically precise, allows to import techniques from S-matrix bootstrap to carve out the landscape of admissible transport, the hydrohedron, and show that self-consistency requires the existence of excitations outside the fluid regime. Based on 2212.07434 and 2305.07703 with Serantes, Spaliński and Withers and on 2007.05524 also with Svensson.
Recent neutron star observations and nuclear physics have supported the picture that the QCD equation of state (EOS) stiffens rapidly from soft EOS at low density to stiff EOS at high density. Such “soft-to-stiff” evolution is difficult to obtain from purely nucleonic calculations relying on many-body forces. Several alternative ideas with the quark degrees of freedom have been suggested, but it is difficult to test the concepts directly. In this respect, QCD-like theories, for which lattice simulations are doable, offer useful laboratories. We study isospin QCD to delineate how the soft-to-stiff evolution occurs, emphasizing the importance of the quark substructure in hadrons. Another important issue is how the EOS approaches to the relativistic or conformal limit at high density (above ~40n0, n0: unit for the nuclear saturation density) where perturbative QCD (pQCD) should be the valid description. We address that, at density of ~40n0, the non-perturbative power corrections to the pQCD is minor in magnitude but still can affect some qualitative trends of EOS, sound velocity and trace anomaly in particular.
The Green's function Monte Carlo (GFMC) method provides accurate
solutions to the nuclear many-body problem and predicts properties of
light nuclei starting from realistic two- and three-body interactions.
Controlling the GFMC fermion-sign problem is crucial, as the
signal-to-noise ratio decreases exponentially with Euclidean time. I
will discuss recent work applying contour deformations to treat this
sign problem and improve the GFMC signal-to-noise ratio.
Proof-of-principle results include achieving an order of magnitude
improvement in the variance of Euclidean density response functions of
the deuteron, paving the way for computing electron- and
neutrino-nucleus cross-sections of larger nuclei.
It is important to unravel the internal structure of neutron stars in astrophysics. Asteroseismology, which analyzes the seismic oscillations of stars, is an effective way to estimate the interior of neutron stars. In asteroseismology, it is known that there are some oscillation modes depending on the transport properties of the stars.
Recently, chiral transport phenomena, which are new types of quantum transports caused by the chirality of relativistic fermions, have attracted considerable interest in the context of the heavy ion collision experiments. One of them is the chiral magnetic effect (CME), which is the current along a magnetic field in the presence of chirality imbalance. The CME leads to the collective excitation called chiral magnetic wave (CMW).
In this talk, we show that the CMW appears in the quark matter inside neutron stars as the seismic oscillation mode (CM-mode). Since the gravitational wave of the CM-mode could be a new probe of the quark matter in neutron stars, we also discuss the frequency and amplitude.
Recently, Hoshina, Fujii, and Kikukawa [1] pointed out that the naive
lattice gauge theory action in Minkowski signature does not result in a
unitary theory in the continuum limit, and Kanwar and Wagman [2]
proposed alternative lattice actions to the Wilson action without
divergences. We here show that the subtlety can be understood from the
asymptotic expansion of the modified Bessel function, which has been
discussed for path integral of compact variables in nonrelativistic
quantum mechanics [3,4]. The essential ingredient for defining the
appropriate continuum theory is the iε prescription, which we show is
applicable also for the Wilson action. It is here important that the iε
should be implemented for both timelike and spacelike plaquettes. We
then argue that such iε can be given a physical meaning that they remove
singular paths having nontrivial winding for an infinitesimal time
evolution that do not have corresponding paths in the continuum. Such
point of view is only apparent in systems with compact variables as
lattice gauge theories.
This talk is based on [5].
[1] H. Hoshina, H. Fujii and Y. Kikukawa, "Schwinger-Keldysh formalism
for Lattice Gauge Theories," PoS LATTICE2019, 190 (2020)
[2] G. Kanwar and M. L. Wagman, "Real-time lattice gauge theory actions:
Unitarity, convergence, and path integral contour deformations," Phys.
Rev. D 104, no.1, 014513 (2021) [arXiv:2103.02602 [hep-lat]]
[3] W. Langguth and A. Inomata, "Remarks on the Hamiltonian path
integral in polar coordinates," J. Math. Phys. 20, 499-504 (1979)
[4] M. Bohm and G. Junker, "Path integration over compact and noncompact
rotation groups," J. Math. Phys. 28, 1978-1994 (1987)
[5] N. Matsumoto "Comment on the subtlety of defining real-time path
integral in lattice gauge theories," [arXiv:2206.00865 [hep-lat]]