Large-N c Gauge Theory and Chiral Random Matrix Theory
We discuss how the $1/N_c$ expansion and the chiral random matrix theory ($\chi$RMT) can be used in the study of large-$N_c$ gauge theories. We first clarify the parameter region in which each of these two approaches is valid: while the fermion mass $m$ is fixed in the standard large-$N_c$ arguments ('t Hooft large-$N_c$ limit), $m$ must be scaled appropriately with a certain negative power of $N_c$ in order for the gauge theories to be described by the $\chi$RMT. Then, although these two limits are not compatible in general, we show that the breakdown of chiral symmetry can be detected by combining the large-$N_c$ argument and the $\chi$RMT with some cares. As a concrete example, we numerically study the four dimensional $SU(N_c)$ gauge theory with $N_f=2$ heavy adjoint fermions, introduced as the center symmetry preserver keeping the infrared physics intact, on a $2^4$ lattice. By looking at the low-lying eigenvalues of the Dirac operator for a massless probe fermion in the adjoint representation, we find that the chiral symmetry is indeed broken with the expected breaking pattern. This result reproduces a well-known fact that the chiral symmetry is spontaneously broken in the pure $SU(N_c)$ gauge theory in the large-$N_c$ and the large-volume limit, and therefore supports the validity of the combined approach. We also provide the interpretation of the gap and unexpected $N_c$-scaling, both of which are observed in the Dirac spectrum.

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: 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: 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: 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: Phased breaking of -t symmetry and leptogenesis
abstract: Nonvanishing U{sub e3} has been theoretically related to a certain flavor symmetry breaking in the neutrino sector. We propose a scenario to break the {mu}-{tau} symmetry so as to accommodate the nonvanishing U{sub e3}. Our scenario is constructed in the context of a seesaw model, and the {mu}-{tau} symmetry breaking is achieved by introducing a CP phase in the Dirac Yukawa matrix. We also show how the deviation of {theta}{sub 23} from the maximal mixing and nonvanishing U{sub e3} depend on the CP phase. Neutrino mixings and the neutrino mass-squared differences are discussed, and the amplitude in neutrinoless double beta decay m{sub ee} are also predicted. We found that a tiny breaking of the {mu}-{tau} symmetry due to mass splitting between two degenerate heavy Majorana neutrinos on top of the Dirac CP phase can lead to successful leptogenesis. We examine how leptogenesis can be related with low energy neutrino measurement, and show that our predictions for U{sub e3} and m{sub ee} can be constrained by the current observation of baryon asymmetry.

title: VI Photometry of Globular Clusters NGC 6293 and NGC 6541: The Formation of the Metal-poor Inner Halo Globular Clusters*
abstract: We present VI photometry of the metal-poor inner halo globular clusters NGC 6293 and NGC 6541 using the WFPC2 on board the Hubble Space Telescope (HST). Our color-magnitude diagrams of the clusters show well-defined blue horizontal-branch populations, consistent with their low metallicities and old ages. NGC 6293 appears to have blue straggler stars in the cluster's central region. We discuss the interstellar reddening and the distance modulus of NGC 6293 and NGC 6541 and obtain E(B - V) = 0.40 and (m - M)0 = 14.61 for NGC 6293 and E(B - V) = 0.14 and (m - M)0 = 14.19 for NGC 6541. Our results confirm that NGC 6293 and NGC 6541 are clearly located in the Galaxy's central regions (RGC ≤ 3 kpc). We also discuss the differential reddening across NGC 6293. The interstellar reddening value of NGC 6293 appears to vary by ΔE(B - V) ≈ 0.02-0.04 mag within our small field of view. The most notable result of our study is that the inner halo clusters NGC 6293 and NGC 6541 essentially have the same ages as M92, confirming the previous result from the HST NIC3 observations of NGC 6287.

title: Radiative corrections to scalar masses and mixing in a scale invariant two Higgs doublet model
abstract: We study the Higgs boson mass spectrum of a classical scale invariant realization of the two Higgs doublet model (SI-2HDM). The classical scale symmetry of the theory is explicitly broken by quantum loop effects due to gauge interactions, Higgs self-couplings and top quark Yukawa couplings. We determine the allowed parameter space compatible with perturbative unitarity and electroweak precision data. Taking into account the LEP and the recent LHC exclusion limits on a standard-model-like Higgs boson HSM, we obtain rather strict constraints on the mass spectrum of the heavy Higgs sector of the SI-2HDM. In particular, if MHSM 125 GeV, the SI-2HDM strongly favors scenarios in which at least one of the nonstandard neutral Higgs bosons has a mass close to 400 GeV and is generically degenerate with the charged Higgs boson, whilst the third neutral Higgs scalar is lighter than 500 GeV.

title: An efficient representation of Euclidean gravity I
abstract: A bstractWe explore how the topology of spacetime fabric is encoded into the local structure of Riemannian metrics using the gauge theory formulation of Euclidean gravity. In part I, we provide a rigorous mathematical foundation to prove that a general Einstein manifold arises as the sum of SU(2)L Yang-Mills instantons and SU(2)R anti-instantons where SU(2)L and SU(2)R are normal subgroups of the four-dimensional Lorentz group Spin(4) = SU(2)L × SU(2)R. Our proof relies only on the general properties in four dimensions: The Lorentz group Spin(4) is isomorphic to SU(2)L × SU(2)R and the six-dimensional vector space Λ2T∗M of two-forms splits canonically into the sum of three-dimensional vector spaces of self-dual and anti-self-dual two-forms, i.e., $ {\Lambda^2}{T^{ * }}M = \Lambda_{ + }^2 \oplus \Lambda_{ - }^2 $. Consolidating these two, it turns out that the splitting of Spin(4) is deeply correlated with the decomposition of two-forms on four-manifold which occupies a central position in the theory of four-manifolds.

title: Higher-order corrections to exclusive production of charmonia at B factories
abstract: As a test of the color-singlet mechanism of the nonrelativistic QCD (NRQCD) factorization approach, we consider the exclusive two-quarkonium productions in electron-positron annihilation e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi at B factories. The cross sections are computed to the next-to-leading order in alpha_s and are resummed to all orders in half the relative velocity v of the charm quark in each meson rest frame. The available theoretical prediction of the cross section for e+ e- -> J/psi + eta_c at the same level of theoretical accuracies is consistent with the available experimental data. Those for e+ e- -> eta_c + gamma and e+ e- -> J/psi + J/psi that are computed new in this work can be tested against the data from future super B factories.