Lattice calculation for unitary fermions in a finite box
A fundamental constant in systems of unitary fermions is the so-called Bertsch parameter, the ratio of the ground state energy for spin paired unitary fermions to that for free fermions at the same density. I discuss how we computed this parameter as well as the pairing gap using a recently developed lattice construction for unitary fermions, by measuring correlation functions for up to 38 fermions in a finite box. Our calculation illustrates interesting issues facing the study of many-body states on the lattice, which may eventually be confronted in QCD calculations as well.

title: Extended study for unitary fermions on a lattice using the cumulant expansion technique
abstract: A recently developed lattice method for large numbers of strongly interacting nonrelativistic fermions exhibits a heavy tail in the distributions of correlators for large Euclidean time {\tau} and large number of fermions N, which only allows the measurement of ground state energies for a limited number of fermions using standard techniques. In such cases, it is suggested that measuring the log of the correlator is more efficient, and a cumulant expansion of this quantity can be exactly related to the correlation function. The cumulant expansion technique allows us to determine the ground state energies of up to 66 unpolarized unitary fermions on lattices as large as 72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic potential on lattices as large as 72$\times$64^3. We have also improved our lattice action with a Galilean invariant form for the four-fermion interaction, which results in predictive volume scaling of the lowest energy of three fermions in a periodic box and in good agreement of our results for N \leq 6 trapped unitary fermions with those from other benchmark calculations.

title: Listening to Noise
abstract: We show how sign problems in simulations of many-body systems can manifest themselves in the form of heavy-tailed correlator distributions, similar to what is seen in electron propagation through disordered media. We propose an alternative statistical approach for extracting ground state energies in such systems, illustrating the method with a toy model and with lattice data for unitary fermions and for baryons in QCD.

title: Large Nc volume reduction and chiral random matrix theory
abstract: Motivated by recent progress on the understanding of the Eguchi-Kawai (EK) volume equivalence and growing interest in conformal window, we simultaneously use the large-Nc volume reduction and Chiral Random Matrix Theory (chRMT) to study the chiral symmetry breaking of four dimensional SU(Nc) gauge theory with adjoint fermions in the large Nc limit. Although some cares are required because the chRMT limit and 't Hooft limit are not compatible in general, we show that the breakdown of the chiral symmetry can be detected in large-Nc gauge theories. As a first step, we mainly focus on the quenched approximation to establish the methodology. We first confirm that heavy adjoint fermions, introduced as the center symmetry preserver, work as expected and thanks to them the volume reduction holds. Using massless overlap fermion as a probe, we then calculate the low-lying Dirac spectrum for fermion in the adjoint representation to compare to that of chRMT, and find that chiral symmetry is indeed broken in the quenched theory.

title: Conformality Lost
abstract: We consider zero-temperature transitions from conformal to non-conformal phases in quantum theories. We argue that there are three generic mechanisms for the loss of conformality in any number of dimensions: (i) fixed point goes to zero coupling, (ii) fixed point runs off to infinite coupling, or (iii) an IR fixed point annihilates with a UV fixed point and they both disappear into the complex plane. We give both relativistic and non-relativistic examples of the last case in various dimensions and show that the critical behavior of the mass gap behaves similarly to the correlation length in the finite temperature Berezinskii-Kosterlitz-Thouless (BKT) phase transition in two dimensions, ξ ∼ exp(c/|T − Tc|). We speculate that the chiral phase transition in QCD at large number of fermion flavors belongs to this universality class, and attempt to identify the UV fixed point that annihilates with the Banks-Zaks fixed point at the lower end of the conformal window.

title: Background electromagnetic fields and nonrelativistic QED matching: Scalar case
abstract: The low-energy structure of hadrons can be described systematically using effective field theory, and the parameters of the effective theory can be determined from lattice QCD computations. Recent work, however, points to inconsistencies between the background field method in lattice QCD and effective field theory matching conditions. We show that the background field problem necessitates inclusion of operators related by equations of motion. In the presence of time-dependent electromagnetic fields, for example, such operators modify Green's functions, thereby complicating the isolation of hadronic parameters which enter on-shell scattering amplitudes. The particularly simple case of a scalar hadron coupled to uniform electromagnetic fields is investigated in detail. At the level of the relativistic effective theory, operators related by equations of motion are demonstrated to be innocuous. The same result does not hold in the non-relativistic effective theory, and inconsistencies in matching are resolved by carefully treating operators related by equations of motion. As uniform external fields potentially allow for surface terms, the problem is additionally analyzed on a torus where such terms are absent. Finite-size corrections are derived for charged scalar correlation functions in uniform electric fields as a useful byproduct.

title: Cosmological Imprint of the Second Law of Thermodynamics
abstract: We study the evolution of the universe in the presence of inflaton, matter, radiation and holographic dark energy. The time evolution of the scale factor is obtained by solving the Friedmann equation of the universe with a good approximation. We present two independent ways which determine the value of the dark energy constant d~1 from the observational data. The two ways are measuring the deceleration parameter and measuring a universal constant depending only on d. The universal constant is given by a dimensionless combination of three scale factors at the equipartition times of radiation–matter, radiation–dark energy and matter–dark energy. We also discuss that the second law of thermodynamics determines the point of time when the dark-energy-dominated era begins in the universe.

title: Near-Infrared Photometry of the Globular Cluster Palomar 6
abstract: We present JHK photometry of Palomar 6. Our photometric measurements range from the red giant branch (RGB) tip to ≈2 mag below the red horizontal branch (RHB), and our color-magnitude diagrams show that Palomar 6 appears to have a well-defined RHB population. The distance modulus and interstellar reddening of the cluster are estimated by comparing the magnitude and color of Palomar 6 RHB stars with those of 47 Tuc. We obtain (m - M)_0 = 14.28 mag and E(B-V) = 1.30 mag for the cluster, and our study suggests that Palomar 6 is clearly located in the Galaxy's central regions. We also discuss the metallicity of the cluster using the slope of the RGB. We obtain [Fe/H] ≈ -1.2 for Palomar 6 and our metallicity estimate is ≈0.5–1.0 dex lower than previous estimates by others.

title: Model independent analysis of the forward–backward asymmetry of top quark production at the Tevatron
abstract: Motivated by a possible anomaly in the forward–backward (FB) asymmetry of top quark ( A FB ) observed at the Tevatron, we perform a model independent analysis on q q ¯ → t t ¯ using an effective Lagrangian with dim-6 four-quark operators. We derive necessary conditions on new physics structures and the couplings that are consistent with the t t ¯ production cross section and A FB measured at the Tevatron, and discuss possible new physics scenarios that could generate such dim-6 operators.

title: Dark energy from vacuum entanglement
abstract: We suggest that vacuum entanglement energy associated with the entanglement entropy of the universe is the origin of dark energy. The observed properties of dark energy can be explained by using the nature of entanglement energy without modification of gravity or exotic matter. From the number of degrees of freedom in the standard model, we obtain the equation of state parameter and for the holographic dark energy, which are consistent with current observational data at the 95% confidence level.

title: Quantum gravity from noncommutative spacetime
abstract: We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative ★-algebra) of quantum gravity.