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We investigate the masses of light pseudoscalar mesons by the method based on a new anomaly free condition for axial vector current. By this viewpoint, the field theories discussed here do not have the $U(1)$ problem. We calculate the masses of nine light pseudoscalar mesons, with theoretical result agrees reasonably good with experiment., Comment: 22 pages, 9 figures

In this paper, we study the problem of trace anomaly for a chiral fermion. To find whether there exists a parity-odd term (Pontryagin term), we use a modified Breitenlohner-Maison-'t Hooft-Veltman regularization and Fujikawa's method by a new Dirac mass term to calculate the trace anomaly for a Weyl fermion coupled to an abelian gauge field and a gravity separately. We show once again that the trace anomaly of energy-momentum tensor for a chiral fermion has Pontryagin term., Comment: 21 pages, 2 figures

We study quantum mechanics problem described by the Schr\"{o}dinger equation with Kapitza pendulum potential, that is the asymmetric double-well potential on the circle. For the oscillatory states spatially localize around the two stable saddle positions of the potential, we obtain the perturbative eigenvalues and corresponding piecewise wavefunctions. The spectrum is computed by extending the angle coordinate to the complex plane so that the quantization condition is formulated as contour integral along a path extending in the imaginary direction. Quantum tunneling between the wells is computed., Comment: v3, 30 pages, 11 figures, a numerical error corrected in (58)(59), journal version

In this paper, we investigate the Pontryagin trace anomaly for chiral fermions in a general curved background using Pauli-Villars regularization. We use both Feynman diagram method and Fujikawa's method to calculate the parity-odd contribution (Pontryagin term). Our result indicates that the trace anomaly of energy-momentum tensor for chiral fermions has Pontryagin term $P=\frac{i}{1536\pi^2}\epsilon_{\nu\sigma\kappa\lambda}R^{\nu\sigma}_{\ \ \rho\mu}R^{\rho\mu\kappa\lambda}$ which agrees with the work of Bonora et al \cite{Bonora:2014qla}., Comment: 20 pages, 6 figures

In this note, we present a new method to investigate the positronium states in ${\rm{QED_3}}$. According to the $\rm{K\ddot{a}ll\acute{e}n-Lehmann}$ spectral representation, the energy eigenvalues of bound states are poles of the correlation function. Using the chain approximation, we obtain the energy eigenvalues of the vector positronium states by taking into account the single-valued branches of multi-valued function. Using the same method, we also find the electron physical mass at some single-valued branch of multi-value function. Our results are agreement with the known ones., Comment: 11 pages, 11 figures

In this paper, we investigate the 1/4 BPS Wilson-'t Hooft loops in $\mathcal{N}$=4 supersymmetric Yang-Mills theory. We use the bulk D3-brane solutions with both electric and magnetic charges on its world-volume to describe some of 1/4 BPS Wilson-'t Hooft loops. The D3-brane supersymmetric solutions are derived form requiring $\kappa$-symmetry. We find the two consistent constraints for Killing spinors and calculate the conserved charges of straight 1/4 BPS Wilson-'t Hooft loops and expectation values of circular 1/4 BPS Wilson-'t Hooft loops separately., Comment: 22 pages

We proved the color reflection relation, U(1)-decoupling, Kleiss-Kuijf and Bern-Carrasco-Johansson relation for color-ordered $\mathcal{N}=4$ Super Yang-Mills theory using $\mathcal{N}=4$ SYM version BCFW recursion relation, which depends only on the general properties of super-amplitudes. This verified the conjectured matter fields BCJ relation. We also show that color reflection relation and U(1)-decoupling relation are special cases of KK relation, if we consider the KK relation as a general relation, then the former two relations come out naturally as the special cases., Comment: 17 pages

Motivated by recently progresses in the study of BCFW recursion relation with nonzero boundary contributions for theories with scalars and fermions\cite{Bofeng}, in this short note we continue the study of boundary contributions of gauge theory with the bad deformation. Unlike cases with scalars or fermions, it is hard to use Feynman diagrams directly to obtain boundary contributions, thus we propose another method based on the ${\cal N}=4$ SYM theory. Using this method, we are able to write down a useful on-shell recursion relation to calculate boundary contributions from related theories. Our result shows the cut-constructibility of gauge theory even with the bad deformation in some generalized sense., Comment: 16 pages, 7 figures

We study several aspects of generalized Janus configuration, which includes a theta term. We investigate the vacuum structure of the theory and find that unlike the Janus configuration without theta term there is no nontrivial vacuum. We also discuss BPS soliton configuration both by supersymmetry analysis and from energy functional. The half BPS configurations could be realized by introducing transverse (p,q)-strings in original brane configuration corresponding to generalized Janus configuration. It turns out the BPS soliton could be taken as modified dyon. We discuss the solution of half BPS equations for the sharp interface case. Moreover we construct less supersymmetric Janus configuration with theta term., Comment: 27 pages; References added

The operator product expansion (OPE) of the Wilson surface operators in six-dimensional (2, 0) superconformal field theory is studied from AdS/CFT correspondence in this paper. We compute the OPE coefficients of the chiral primary operators using the M5-brane description for spherical Wilson surface operators in higher dimensional representations. We use the non-chiral M5-brane action in our calculation. We also discuss their membrane limit, and compare our results with the ones obtained from membrane description., Comment: 27 pages, no figures; typos corrected, references added, minor changes, 29 pages; typos fixed, JHEP published version

This paper has been withdrawn by the author due to a crucial sign error in equation 1., Comment: This paper has been withdrawn