[Paper Review] The Large Vector Multiplet Action

Itai Ryb|ArXiv.org|Oct 17, 2007

Black Holes and Theoretical Physics33 references8 citations

TL;DR

This paper proposes two consistent actions for the $d=2,~{}N=(2,2)$ large vector multiplet by eliminating higher-derivative terms via field redefinitions and gauge-invariant field-strengths. It constructs kinetic terms for scalar and spinor invariants, including topological terms, and derives modified matter couplings, providing a foundation for generalized Kähler geometry in nonlinear sigma models.

ABSTRACT

We discuss possible actions for the d=2, N=(2,2) large vector multiplet that gauges isometries of generalized Kahler geometries. We explore two scenarios that allow us to write kinetic and superpotential terms for the scalar field-strengths, and write kinetic terms for the spinor invariants that can introduce topological terms for the connections.

Motivation & Objective

• To resolve the challenge of higher-derivative terms in the large vector multiplet action, which arise from four extra spinor multiplets.
• To construct kinetic and superpotential terms for scalar field-strengths in the context of generalized Kähler geometry.
• To formulate first-derivative actions for spinor invariants, including topological terms for gauge connections.
• To ensure consistency with T-duality and generalized Kähler quotients by using field redefinitions and gauge-invariant combinations.
• To enable future applications in $H$-flux GLSMs and mirror symmetry through a well-defined multiplet structure.

Proposed method

• Uses field redefinitions to eliminate higher-derivative terms in the action, specifically transforming the $N=(1,1)$ spinor invariants.
• Constructs kinetic terms for scalar field-strengths using chiral and twisted chiral superfields, ensuring first-derivative structure.
• Applies gauge-invariant combinations of $N=(2,2)$ supercovariant derivatives to define field-strengths $W, B, \tilde{W}, \tilde{B}$ and their conjugates.
• Derives modified matter couplings by projecting the Kähler potential to $N=(1,1)$ superspace and redefining fields to remove higher derivatives.
• Utilizes matrix transformations $L = M \cdot \Xi$ to relate $N=(2,2)$ invariants to $N=(1,1)$ fields, enabling consistent action construction.
• Considers two scenarios: one with chiral field-strengths and one with twisted chiral field-strengths, both yielding first-derivative actions.

Experimental results

Research questions

• RQ1 How can higher-derivative terms be systematically removed from the large vector multiplet action in $N=(2,2)$ supersymmetry?
• RQ2 What are the consistent kinetic and superpotential terms for scalar field-strengths in the large vector multiplet?
• RQ3 How do field redefinitions and gauge invariants allow for a first-derivative action for spinor invariants?
• RQ4 What is the role of T-duality in relating the large vector multiplet to semichiral multiplets and generalized Kähler geometry?
• RQ5 How do matter couplings transform under field redefinitions that eliminate higher derivatives?

Key findings

• Two unique abelian actions for the large vector multiplet are constructed, both free of higher-derivative terms via field redefinitions.
• Kinetic terms for scalar field-strengths are built from chiral and twisted chiral invariants, ensuring first-derivative structure.
• Spinor invariants admit kinetic terms that describe twisted conformal field theories and topological terms for gauge connections.
• Field redefinitions relate the $N=(1,1)$ components $\hat{q}^{\phi}, \hat{q}^{\chi}, \hat{q}^{\prime}, A_{\pm}$ in the chiral and twisted chiral scenarios, ensuring equivalence in the quotient.
• The action remains consistent under T-duality when linear terms constrain field-strengths to vanish, yielding a standard $\sigma$-model form.
• The modified matter couplings are derived explicitly, showing how superpotential and kinetic terms transform under the field redefinitions.