[Paper Review] Modified N=2 supersymmetry and Fayet-Iliopoulos terms

E. A. Ivanov, Б. М. Зупник|arXiv (Cornell University)|Oct 30, 1997

Black Holes and Theoretical Physics20 citations

TL;DR

This paper investigates modified N=2 supersymmetry in abelian gauge theories with dual electric and magnetic Fayet-Iliopoulos (FI) terms using manifestly supersymmetric superfield formulations. It shows that introducing both FI terms stabilizes off-shell partial supersymmetry breaking, leading to a modified N=2 superalgebra where closure requires special gauge transformations before gauge-fixing. The key result is that the N=2 supersymmetry algebra is intrinsically modified on gauge-variant objects like prepotentials, with implications for matter coupling and duality invariance.

ABSTRACT

We study peculiarities of realization of N=2 supersymmetry in N=2 abelian gauge theory with two sorts of FI terms, electric and magnetic ones, within manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic prepotentials. We obtain a `magnetic', duality- transformed superfield form of the N=2 Maxwell effective holomorphic action with standard electric $FI$ term and demonstrate that in such a system off-shell N=2 supersymmetry is inevitably realized in an unusual Goldstone mode corresponding to the {\it partial} spontaneous breaking down to N=1. On shell, the standard total breaking occurs. In a system with the two sorts of FI terms, off-shell N=2 supersymmetry is realized in the partial breaking mode both in the electric and magnetic representations. This regime is retained on shell due to the Antoniadis- Partouche-Taylor mechanism. We show that the off-shell algebra of N=2 supersymmetry in the partial breaking realization is modified on gauge-variant objects like potentials and prepotentials. The closure of spinor charges involves some special gauge transformations before any gauge-fixing.

Motivation & Objective

• To analyze the realization of N=2 supersymmetry in abelian gauge theories with both electric and magnetic FI terms using manifestly off-shell superfield formulations.
• To investigate how duality transformations affect the structure of N=2 supersymmetry and its realization in the presence of FI terms.
• To determine whether off-shell partial supersymmetry breaking is stable under duality and preserved on-shell via the Antoniadis-Partouche-Taylor mechanism.
• To examine the modification of the N=2 superalgebra when acting on gauge-variant objects such as harmonic-analytic prepotentials.
• To address the challenges in constructing minimal couplings of matter hypermultiplets to the modified N=2 gauge prepotential.

Proposed method

• Utilizes the Mezincescu prepotential and harmonic-analytic superfield formalism to describe N=2 abelian gauge theories with FI terms.
• Applies duality transformations to convert the standard electric FI term into a magnetic FI term, analyzing the resulting superfield action.
• Derives modified N=2 supersymmetry transformation laws for the harmonic-analytic prepotential $V^{++}$, showing closure requires additional gauge transformations.
• Analyzes the algebraic closure of N=2 supercharges, demonstrating that anticommutators include non-trivial gauge transformations before any gauge-fixing.
• Constructs the modified N=2 superalgebra with structure constants involving $M^{ik}$ and $E^{ik}$, breaking SU(2) to U(1) and introducing central charges.
• Assesses the incompatibility of standard minimal couplings $\bar{q}^+(D^{++}+iV^{++}_s)q^+$ with the modified supersymmetry transformations.

Experimental results

Research questions

• RQ1 How does the presence of both electric and magnetic FI terms affect the off-shell realization of N=2 supersymmetry?
• RQ2 What is the algebraic structure of N=2 supersymmetry when the theory includes dual FI terms, and how does it differ from the standard algebra?
• RQ3 Why is the closure of the N=2 superalgebra on the harmonic-analytic prepotential $V^{++}$ dependent on special gauge transformations before gauge-fixing?
• RQ4 Can the standard minimal coupling of matter hypermultiplets to $V^{++}$ be preserved under the modified N=2 supersymmetry transformations?
• RQ5 How does the Antoniadis-Partouche-Taylor mechanism ensure that partial supersymmetry breaking is preserved on-shell in the dual formulation?

Key findings

• Off-shell N=2 supersymmetry is necessarily realized in a partial breaking mode when both electric and magnetic FI terms are present, with the symmetry breaking pattern $N=2 \to N=1$.
• In the dual 'magnetic' formulation with only an electric FI term, off-shell N=2 supersymmetry is modified and realized as partial breaking, with the superfield strength acquiring an inhomogeneous transformation.
• The modified N=2 superalgebra includes non-trivial gauge transformations in the anticommutator of spinor charges, even before gauge-fixing, due to the presence of FI terms.
• The automorphism group SU(2) is explicitly broken to U(1) in the modified algebra, with structure constants involving $M^{ik}$ or $E^{ik}$.
• The standard minimal coupling $\bar{q}^+(D^{++}+iV^{++}_s)q^+$ is not invariant under the modified N=2 supersymmetry transformations, indicating a fundamental obstruction to matter coupling.
• The modified superalgebra contains a central charge proportional to the global U(1) generator, which commutes with all gauge generators but acts non-trivially on charged matter multiplets.