Massive Hypermultiplets Research Articles

Effective action of the N = 2 Maxwell multiplet in harmonic superspace

We present, in the N=2, D=4 harmonic superspace formalism, a general method for constructing the off-shell effective action of an N=2 abelian gauge superfield coupled to matter hypermultiplets. Using manifestly N=2 supersymmetric harmonic supergraph techniques, we calculate the low-energy corrections to the renormalized one-loop effective action in terms of N=2 (anti)chiral superfield strengths. For a harmonic gauge prepotential with vanishing vacuum expectation value, corresponding to massless hypermultiplets, the only non-trivial radiative corrections to appear are non-holomorphic. For a prepotential with non-zero vacuum value, which breaks the U(1)-factor in the N=2 supersymmetry automorphism group and corresponds to massive hypermultiplets, only non-trivial holomorphic corrections arise at leading order. These holomorphic contribution are consistent with Seiberg's quantum correction to the effective action, while the first non-holomorphic contribution in the massless case is the N=2 supersymmetrization of the Heisenberg-Euler effective Lagrangian.

Periods and Prepotential of N = 2 SU(2) Supersymmetric Yang–Mills Theory with Massive Hypermultiplets

We derive a simple formula for the periods associated with the low energy effective action of N = 2 supersymmetric SU(2) Yang–Mills theory with massive Nf ≤ 3 hypermultiplets. This is given by evaluating explicitly the integral associated to the elliptic curve using various identities of hypergeometric functions. Following this formalism, we can calculate the prepotential with massive hypermultiplets both in the weak coupling region and in the strong coupling region. In particular, we show how the Higgs field and its dual field are expressed as generalized hypergeometric functions when the theory has a conformal point.

Prepotentials of N=2 SU(2) Yang–Mills theories coupled with massive matter multiplets

We discuss N=2 SU(2) Yang–Mills gauge theories coupled with Nf(=2,3) massive hypermultiplets in the weak coupling limit. We determine the exact massive prepotentials and the monodromy matrices around the weak coupling limit. We also study that the double scaling limit of these massive theories and find that the massive Nf−1 theory can be obtained from the massive Nf theory. New formulae for the massive prepotentials and the monodromy matrices are proposed. In these formulae, Nf dependences are clarified.

Multi-instanton calculus in N=2 supersymmetric gauge theory. II. Coupling to matter.

We further discuss the $N=2$ superinstantons in SU(2) gauge theory, obtained from the general self-dual solutions of topological charge $n$ constructed by Atiyah, Drinfeld, Hitchin, and Manin (ADHM). We realize the $N=2$ supersymmetry algebra as actions on the superinstanton moduli. This allows us to recast in concise superfield notation our previously obtained expression for the exact classical interaction between $n$ ADHM superinstantons mediated by the adjoint Higgs bosons, and, moreover, to incorporate ${N}_{F}$ flavors of hypermultiplets. We perform explicit one- and two-instanton checks of the Seiberg-Witten prepotentials for all ${N}_{F}$ and arbitrary hypermultiplet masses. Our results for the low-energy couplings are all in precise agreement with the predictions of Seiberg and Witten except for ${N}_{F}=4$, where we find a finite renormalization of the coupling which is absent in the proposed solution.

A two-instanton test of the exact solution of N = 2 supersymmetric QCD

The exact solution of N = 2 supersymmetric QCD found by Seiberg and Witten includes a prediction for all multi-instanton contributions to the low-energy dynamics. In the case where the matter hypermultiplets are massless, the leading non-perturbative contribution at weak coupling comes from the two-instanton sector. We calculate this contribution from first principles using the exact two-instanton solution of the self-dual Yang-Mills equation found by Atiyah, Drinfeld, Hitchin and Manin. We find exact agreement with the predictions of Seiberg and Witten for all numbers of flavours. We also confirm their predictions for the case of massive hypermultiplets.

Integrable structure in supersymmetric gauge theories with massive hypermultiplets

We study the quantum moduli space of vacua of N = 2 supersymmetric SU( N c ) gauge theories coupled to N f flavors of quarks in the fundamental representation. We identify the moduli space of the N c = 3 and N f = 2 massless case with the full spectral curve obtained from the Lax representation of the Goryachev-Chaplygin top. For the case with massive quarks, we present an integrable system where the corresponding hyperelliptic curve parametrizing the Laurent solution coincides with that of the moduli space of N c = 3 with N f = 0, 1, 2. We discuss possible generalizations of the integrable systems relevant to gauge theories with N c ≠ 3 and general N f .

Master formula of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets

Master formula of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets

On the relation between the holomorphic prepotential and the quantum moduli in SUSY gauge theories

We give a simple proof of the relation Λ∂ ΛF = i 2π b 1〈 TrΦ 2〉 , which is valid for N = 2 supersymmetric QCD with massless quarks. We consider SU( N c ) gauge theories as well as SO( N c ) and SP( N c ). An analogous relation which corresponds to massive hypermultiplets is written down. We also discuss the generlizations to N = 1 models in the Coulomb phase.

N = 2 harmonic superspace with central charges and its application to self-interacting massive hypermultiplets

We investigate the structure of the harmonic superspace formalism with central charges for N = 2 supersymmetry, which is applicable to a wide class of N = 2 theories. As a simple application, the Lagrangian for self-interacting N = 2 massive scalar hypermultiplets is constructed in this formalism, and the interactions are explicitly obtained in terms of physical fields in the lowest order in the coupling constant. Although the theory looks highly unrenormalizable, remarkable cancellations take place so that all radiative corrections vanish in the lowest nontrivial order in the coupling constant.

N = 2 harmonic superspace with central charges and its application to self-interacting massive hypermultiplets: Nobuyoshi Ohta, Theory Group, Department of Physics, University of Texas, Austin, Texas 78712; and Hiroaki Sugata and Hiroshi Yamaguchi, Institute of Physics, College of General Education, Osaka University, Toyonaka 560, Japan

N = 2 harmonic superspace with central charges and its application to self-interacting massive hypermultiplets: Nobuyoshi Ohta, Theory Group, Department of Physics, University of Texas, Austin, Texas 78712; and Hiroaki Sugata and Hiroshi Yamaguchi, Institute of Physics, College of General Education, Osaka University, Toyonaka 560, Japan

N=2 extended supersymmetric GUTs

Abstract We construct N =2 extended SUSY GUTs which provide a general association between massive spin-1 gauge bosons, spin - 1 2 inos and spin-0 Higgs bosons. The corresponding gauge hypermultiplets are of four different types: 1. (i) massless the photon, 2 Majorana photinos and 2 real spin-0 photons the gluons, 2 octet Majorana gluinos and 2 real octet spin-0 gluons 2. (ii) massive type I: e.g. the W ± , 4 Dirac winos and 5 charged Higgs bosons the Z, 4 Dirac winos and 5 neutral Higgs bosons 3. (iii) massive type II: e.g. the X ± 4 3 , 2 Dirac xinos and 1 charged triplet Higgs boson; 4. (iv) massive type III: e.g. the Y ± 1 3 , 4 Dirac yinos and 5 charged triplet Higgs bosons; while leptons and quarks are associated with mirror and spin-0 partners. The anticommutators of the two supersymmetry generators provide two spin-0 symmetry generators Z s and Z p , which do not commute. Their field-independent parts 〈 Z s 〉 and 〈 Z p rang; do commute, however, and appear as central charges in the symmetry algebra of the spontaneously broken gauge theory . These central charges 〈 Z s 〉 and 〈 Z p 〉 are linear combinations of global symmetry generators with grand unification generators such as the weak hypercharge (but not the electrical charge!). They survive the electroweak symmetry breaking. They do not vanish for massive gauge hypermultiplets of types II and III, which verify M 2 =〈Z s 〉 2 +〈Z p 〉 2 >0 and M 2 >〈Z s 〉 2 +〈Z p 〉 2 >0 , respectively. The formula M 2 ≅〈Z s 〉 2 +〈Z p 〉 2 determines the mass spectrum on the grand unification scale, up to electroweak corrections. Finally, we indicate how our mass relations can be interpreted in a 5- or 6-dimensional formalism, the central charges appearing as the extra components of the covariant momentum along the compact fifth or sixth dimensions; and how to evaluate the grand unification mass m x in terms of the lengths of the latter ( m x ∼ℏ/ L 5(6) c ).

Quartic mass matrix and renormalization constants in supersymmetric Yang-Mills theories

We derive the general formula for the supertrace of the quartic mass matrix in a general supersymmetric gauge theory, with arbitrary representations for the chiral multiplets. This formula clarifies the non-renormalization theorems in presence of gauge interactions and gives “extended renormalization theorems” for N = 2 and N = 4 supersymmetric Yang-Mills theories. In particular we find the known result that g ren = g bare for the N = 4 theory and the new result m ren = m bare for the N = 2 gauge interactions of massive hypermultiplets. We give arguments to the extent that the latter non-renormalization theorem persists to all orders in perturbation theory.