Thermodynamics of free domain wall and overlap fermions

I give a brief introduction to the goals, challenges, and technical difficulties of lattice QCD thermodynamics and present some recent results from the HotQCD collaboration for the crossover temperature, equation of state, and other observables.

We calculate the 2-loop partition function of QCD on the lattice, using the Wilson formulation for gluons and the overlap-Dirac operator for fermions. Direct by-products of our result are the 2-loop free energy and average plaquette. Our calculation serves also as a prototype for further higher loop calculations in the overlap formalism. We present our results as a function of a free parameter $M_0$ entering the overlap action; the dependence on the number of colors $N$ and f...

We perform the first study of lattice QCD with overlap fermions at finite temperature $T$ and chemical potential $\mu$. We start from the Taylor expanded overlap fermion action, and derive in the strong coupling limit the effective free energy by mean field approximation. On the ($\mu,T$) plane and in the chiral limit, there is a tricritical point, separating the second order chiral phase transition line at small $\mu$ and large $T$, and first order chiral phase transition li...

I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum, weak matrix elements, the $n_f=2$ finite temperature phase transition, and topology and zero modes and conclude with topics for future study.

In this talk I review the current status of lattice QCD calculations at nonzero temperature and density. I focus on the QCD phase structure and bulk QCD thermodynamics at zero and nonzero chemical potentials.

We study free particles in a one-dimensional box with combinations of two types of boundary conditions: the Dirichlet condition and a one-parameter family of quasi-Neumann conditions at the two walls. We calculate energy spectra approximately and obtain equations of state having the same (one-dimensional) volume dependence as van der Waals equations of state. The dependence of the equations of state is examined for particles obeying Maxwell-Boltzmann, Bose-Einstein, or Fermi-...

The beta-shift induced from dynamical domain wall quarks leads to increased roughness of the gauge field, thus reversing the effect of smoothing from the gauge action improvement. By exploiting the relation of overlap and domain wall fermions in greater detail,we propose an algorithm which reduces the beta-shift to the level of dynamical overlap fermions.

We compute thermal and quantum fluctuations in the background of a domain wall in a scalar field theory at finite temperature using the exact scalar propagator in the subspace orthogonal to the wall's translational mode. The propagator makes it possible to calculate terms of any order in the semiclassical expansion of the partition function of the system. The leading term in the expansion corresponds to the fluctuation determinant, which we compute for arbitrary temperature i...

We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also di...

We present a formulation of domain-wall fermions in the Schr\"odinger functional by following a universality argument. To examine the formulation, we numerically investigate the spectrum of the free operator and perform a one-loop analysis to confirm universality and renormalizability. We also study the breaking of the Ginsparg-Wilson relation to understand the structure of chiral symmetry breaking from two sources: The bulk and boundary. Furthermore, we discuss the lattice a...