Nonabelian 2-forms and loop space connections from SCFT deformations

Abstract

It is shown how the deformation of the superconformal generators on the string's worldsheet by a nonabelian super-Wilson line gives rise to a covariant exterior derivative on loop space coming from a nonabelian 2-form on target space. The expression obtained this way is new in the context of strings, and its consistency is verified by checking that its global gauge transformations on loop space imply the familiar gauge transformations on target space. We derive the second order gauge transformation from infinitesimal local gauge transformations on loop space and find that a consistent picture is obtained only when the sum of the 2-form and the 1-form field strengths vanish. The same condition has recently been derived from 2-group gauge theory reasoning. We observe that this condition implies that the connection on loop space is flat, which is a crucial sufficient condition for the nonabelian surface holonomy induced by it to be well defined. Finally we compute the background equations of motion of the nonabelian 2-form by canceling divergences in the deformed boundary state.

34 pages, general discussion of flat loop space connections added, references added, background material and clarifications added

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Cited by in corpus (7)

• A Non-Abelian Self-Dual Gauge Theory in 5+1 Dimensions
• Non-Abelian Chiral 2-Form and M5-Branes
• From Loop Space Mechanics to Nonabelian Strings
• A reparametrization invariant surface ordering
• Topological Quantum Field Theory on Non-Abelian Gerbes
• Super-Pohlmeyer invariants and boundary states for non-abelian gauge fields
• Strings with extended non-Abelian gauge interaction