Hyunsoo Min

Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay

We present a general numerical method for computing precisely the false vacuum decay rate, including the prefactor due to quantum fluctuations about the classical bounce solution, in a self-interacting scalar field theory modeling the process of nucleation in four-dimensional space-time. This technique does not rely on the thin-wall approximation. The method is based on the Gelfand-Yaglom approach to determinants of differential operators, suitably extended to higher dimensions using angular momentum cutoff regularization. A related approach has been discussed recently by Baacke and Lavrelashvili, but we implement the regularization and renormalization in a different manner, and compare directly with analytic computations made in the thin-wall approximation. We also derive a simple new formula for the zero mode contribution to the fluctuation prefactor, expressed entirely in terms of the asymptotic behavior of the classical bounce solution.

Generalized dynamical spin chain and 4-loop integrability in N=6 superconformal Chern–Simons theory

Abstract We revisit unitary representation of centrally extended psu ( 2 | 2 ) excitation superalgebra. We find most generally that ‘pseudo-momentum’, not lattice momentum, diagonalizes spin chain Hamiltonian and leads to generalized dynamic spin chain. All known results point to lattice momentum diagonalization for N = 4 super-Yang–Mills theory. Having different interacting structure, we ask if N = 6 superconformal Chern–Simons theory provides an example of pseudo-momentum diagonalization. For SO ( 6 ) sector, we study maximal shuffling and next-to-maximal shuffling terms in the dilatation operator and compare them with results expected from psu ( 2 | 2 ) superalgebra and integrability. At two loops, we rederive maximal shuffling term (3-site) and find perfect agreement with known results. At four loops, we first find absence of next-to-maximal shuffling term (4-site), in agreement with prediction based on integrability. We next extract maximal shuffling term (5-site), the most relevant term for checking the possibility of pseudo-momentum diagonalization. Curiously, we find that result agrees with integrability prediction based on lattice momentum, as in N = 4 super-Yang–Mills theory. Consistency of our results is fully ensured by checks of renormalizability up to six loops.

Schrödinger fields on the plane with [U(1)]N Chern-Simons interactions and generalized self-dual solitons

A general nonrelativistic field theory on the plane with couplings to an arbitrary number of Abelian Chern-Simons gauge fields is considered. Elementary excitations of the system are shown to exhibit fractional and mutual statistics. We identify the self-dual systems for which certain classical and quantal aspects of the theory can be studied in a much simplified mathematical setting. Then, specializing to the general self-dual system with two Chern-Simons gauge fields (and nonvanishing mutual statistics parameter), we present a systematic analysis for the static vortexlike classical solutions, with or without a uniform background magnetic field. Relativistic generalizations are also discussed briefly.

Precise Quark-Mass Dependence of the Instanton Determinant

The fermion determinant in an instanton background for a quark field of arbitrary mass is determined exactly using an efficient numerical method to evaluate the determinant of a partial-wave radial differential operator. The bare sum over partial waves is divergent but can be renormalized in the minimal subtraction scheme using the result of WKB analysis of the large partial-wave contribution. Previously, only a few leading terms in the extreme small and large mass limits were known for the corresponding effective action. Our approach works for any quark-mass and interpolates smoothly between the analytically known small and large mass expansions.

Massive field contributions to the QCD vacuum tunneling amplitude

For the one-loop contribution to the QCD vacuum tunneling amplitude by quarks of generic mass value, we make use of a calculational scheme exploiting a large mass expansion together with a small mass expansion. The large mass expansion for the effective action is given by a series involving higher-order Seeley-DeWitt coefficients, and we carry this expansion up to order

Calculation of QCD instanton determinant with arbitrary mass

1/(m\rho)^8

Moduli space dimensions of multipronged strings

, where

Dynamics of BPS states in the Dirac-Born-Infeld theory

m

Scattering of solitons in the derivative nonlinear Schrödinger model

denotes mass of the quark and

Instanton determinant with arbitrary quark mass: WKB phase-shift method and derivative expansion

\rho