Multiscalar production amplitudes beyond threshold

We present exact tree-order amplitudes for $H^* \to n~H$, for final states containing one or two particles with non-zero three-momentum, for various interaction potentials. We show that there are potentials leading to tree amplitudes that satisfy unitarity, not only at threshold but also in the above kinematical configurations and probably beyond. As a by-product, we also calculate $2\to n$ tree amplitudes at threshold and show that for the unbroken $\phi^4$ theory they vanish for $n>4~$, for the Standard Model Higgs they vanish for $n\ge 3~$ and for a model potential, respecting tree-order unitarity, for $n$ even and $n>4~$. Finally, we calculate the imaginary part of the one-loop $1\to n$ amplitude in both symmetric and spontaneously broken $\phi^4$ theory.Comment: 11 pages, Latex, 3 figures (available on request

On amplitude zeros at threshold

The occurrence of zeros of 2 to n amplitudes at threshold in scalar theories is studied. We find a differential equation for the scalar potential, which incorporates all known cases where the 2 to n amplitudes at threshold vanish for all sufficiently large $n$, in all space-time dimensions, $d\ge 1$. This equation is related to the reflectionless potentials of Quantum Mechanics and to integrable theories in 1+1 dimensions. As an application, we find that the sine-Gordon potential and its hyperbolic version, the sinh-Gordon potential, also have amplitude zeros at threshold, ${\cal A}(2\to n)=0$, for $n\ge 4$ and $d\ge 2$, independently of the mass and the coupling constant.Comment: 6 pages, Latex, CERN-TH.6762/9

Sp(N) higher-derivative F-terms via singular superpotentials

We generalize the higher-derivative F-terms introduced by Beasley and Witten (hep-th/0409149) for SU(2) superQCD to Sp(N) gauge theories with fundamental matter. We generate these terms by integrating out massive modes at tree level from an effective superpotential on the chiral ring of the microscopic theory. Though this superpotential is singular, its singularities are mild enough to permit the unambiguous identification of its minima, and gives sensible answers upon integrating out massive modes near any given minimum.Comment: 15 pages, 6 figure

Comments on scaling limits of 4d N=2 theories

We revisit the study of the maximally singular point in the Coulomb branch of 4d N=2 SU(N) gauge theory with N_f=2n flavors for N_f= 2, we find that the low-energy physics is described by two non-trivial superconformal field theories coupled to a magnetic SU(2) gauge group which is infrared free. (In the special case n=2, one of these theories is a theory of free hypermultiplets.) This observation removes a possible counter example to a conjectured a-theorem.Comment: 13 page

The Coulomb branch of N=1 supersymmetric SU(N_c) x SU(N_c) gauge theories

We analyze the low energy behavior of N=1 supersymmetric gauge theories with SU(N_c) x SU(N_c) gauge group and a Landau-Ginzburg type superpotential. These theories contain fundamentals transforming under one of the gauge groups as well as bifundamental matter which transforms as a fundamentals under each. We obtain the parametrization of the gauge coupling on the Coulomb branch in terms of a hyperelliptic curve. The derivation of this curve involves making use of Seiberg's duality for SQCD as well as the classical constraints for N_f=N_c+1 and the quantum modified constraints for N_f=N_c.Comment: 16 pages, no figures, revtex; typos correcte

On singular effective superpotentials in supersymmetric gauge theories

We study N=1 supersymmetric SU(2) gauge theory in four dimensions with a large number of massless quarks. We argue that effective superpotentials as a function of local gauge-invariant chiral fields should exist for these theories. We show that although the superpotentials are singular, they nevertheless correctly describe the moduli space of vacua, are consistent under RG flow to fewer flavors upon turning on masses, and also reproduce by a tree-level calculation the higher-derivative F-terms calculated by Beasely and Witten (hep-th/0409149) using instanton methods. We note that this phenomenon can also occur in supersymmetric gauge theories in various dimensions.Comment: 21 pages, 5 figures; minor errors correcte

Zero-dimensional field theory

A study of zero-dimensional theories, based on exact results, is presented. First, relying on a simple diagrammatic representation of the theory, equations involving the generating function of all connected Green's functions are constructed. Second, exact solutions of these equations are obtained for several theories. Finally, renormalization is carried out. Based on the anticipated knowledge of the exact solutionsthe full dependence on the renormalized coupling constant is studied.Comment: 38 pages, LaTe

Argyres-Douglas Loci, Singularity Structures and Wall-Crossings in Pure N=2 Gauge Theories with Classical Gauge Groups

N=2 Seiberg-Witten theories allow an interesting interplay between the Argyres-Douglas loci, singularity structures and wall-crossing formulae. In this paper we investigate this connection by first studying the singularity structures of hyper-elliptic Seiberg-Witten curves for pure N=2 gauge theories with SU(r+1) and Sp(2r) gauge groups, and propose new methods to locate the Argyres-Douglas loci in the moduli space, where multiple mutually non-local BPS states become massless. In a region of the moduli space, we compute dyon charges for all 2r+2 and 2r+1 massless dyons for SU(r+1) and Sp(2r) gauge groups respectively for rank r>1. From here we elucidate the connection to the wall-crossing phenomena for pure Sp(4) Seiberg-Witten theory near the Argyres-Douglas loci, despite our emphasis being only at the massless sector of the BPS spectra. We also present 2r-1 candidates for the maximal Argyres-Douglas points for pure SO(2r+1) Seiberg-Witten theory.Comment: 81 pages, 41 figures, LaTeX; v2: Minor cosmetic changes and correction of a typographical error in acknowledgement. Final version to appear in JHE

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde