Haru-Tada Sato

Multiloop world-line Green functions from string theory

Abstract We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a Φ 3 particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop Φ 3 diagram.

Thermodynamic Gross-Neveu model in a constant electromagnetic field

We analyze the effective potential of the D-dimensional thermodynamic Gross-Neveu model (defined by large-N leading order, 2 ⩽ D < 4) in a constant electromagnetic field (E · B = 0). The potential is derived from a thermal analogy of the worldline formalism. In the magnetic case, the potential is expressed in terms of a discretized momentum sum instead of a continuum momentum integral, and it reproduces the known critical values of μ and T in the continuum limit. In the electric case, chiral symmetry is restored at finite T (with arbitrary μ) against instability of the fermion vacuum. An electromagnetic duality is pointed out as well. Phase diagrams are obtained in both cases.

Exact combinatorics of Bern-Kosower-type amplitudes for two-loop φ3 theory

Abstract Counting the contribution rate of a world-line formula to Feynman diagrams in ( φ 3 theory, we explain the idea of how to determine precise combinatorics of Bern-Kosower-like amplitudes derived from a bosonic string theory for N -point two-loop Feynman amplitudes. In this connection we also present a method to derive simple and compact world-line forms for the effective action.

Relation between worldline Green functions for scalar two-loop diagrams

Abstract We discuss the relation between two-loop bosonic worldline Green functions which are obtained by Schmidt and Schubert in two different parametrizations of a two-loop worldline. These Green functions are transformed into each other by some transformation rules based on reparametrizations of the proper time and worldline modular parameters.

OPE formulae for deformed super-Virasoro algebras

We show the OPE formulae for three types of deformed super-Virasoro algebras: the Chaichian-Presnajder deformation, the Belov-Chaltikhian deformation and its modified version. Fundamental (anti-) commutation relations toward a ghost realization of deformed super-Virasoro algebra are also discussed.

Pinched gluon vertex operator in the super world-line formalism

Abstract We reformulate, using the super world-line formalism, the pinched gluon vertex operator proposed by Strassler. The pinched vertex operator turns out to be the product of two gluon vertex operators with the insertion of a δ-function which makes the super distances between them zero. Thus the pinch procedures turn out to be nothing but the insertions of δ-functions. Applying our formulation to two-loop diagrams which are the QED correction to gluon scatterings via a single spinor loop, with the QED charge e being replaced by the strong coupling g, we give various formulae on pinched N-point functions.

Deformation of super Virasoro algebra in noncommutative quantum superspace

Abstract We present a twisted commutator deformation for N = 1,2 super Virasoro algebras based on GL q (1,1) covariant noncommutative superspace.

Integral representations of thermodynamic 1PI Green’s functions in the world-line formalism

The issue discussed is a thermodynamic version of the Bern–Kosower master amplitude formula, which contains all necessary one-loop Feynman diagrams. It is demonstrated how the master amplitude at finite values of temperature and chemical potential can be formulated within the framework of the world-line formalism. In particular we present an elegant method of how to introduce a chemical potential for a loop in the master formula. Various useful integral formulas for the master amplitude are then obtained. The nonanalytic property of the master formula is also derived in the zero temperature limit with the value of chemical potential kept finite.

World-line Green functions with momentum and source conservations

Based on the generating functional method with an external source function, a useful constraint on the source function is proposed for analyzing the one- and two-loop world-line Green functions. The constraint plays the same role as the momentum conservation law of a certain nontrivial form, and transforms ambiguous Green functions into the uniquely defined Green functions. We also argue reparametrizations of the Green functions defined on differently parameterized world-line diagrams.

Thermodynamic fermion loop in a constant magnetic field

The one-loop effective potential of a thermodynamic fermion loop in a constant magnetic field is studied. As expected, it can be interpreted literally as a discretized sum of (D−2)-dimensional energy density above the Dirac sea. Large/small mass expansions of the potential are also examined.