The geometry of gauged (super)conformal mechanics

Abstract

Motivated by recently explored examples, we undertake a systematic study of conformal invariance in one-dimensional sigma models where an isometry group has been gauged. Perhaps surprisingly, we uncover classes of sigma models which are only scale invariant in their ungauged form and become fully conformally invariant only after gauging. In these cases the target space of the gauged sigma model satisfies a deformation of the well-known conformal geometry constraints. We consider bosonic models as well as their $$ \mathcal{N} $$ N = 1, 2, 4 supersymmetric extensions. We solve the quantum ordering ambiguities in implementing (super-) conformal symmetry on the physical Hilbert space. Examples of our general results are furnished by the D(2, 1; 0)-invariant Coulomb branch quiver models relevant for black hole physics.

Gauged (Super)Conformal Models

“…It is just through gauging (part of) their isometries that they can admit full conformal invariance via the existence of ξ ⊥ , which satisfies (17). • An application of, and motivation for, the work of [4] is provided by the Coulomb branch quiver mechanics describing the dynamics of D-brane systems in an AdS 2 scaling limit. As a special class, these systems exhibit D(2, 1; 0) symmetry [6].…”

“…Acknowledgments: This article is a part of the work of Ref. [4], accomplished in collaboration with D. Van den Bleeken, J. Raeymaekers and C. Şanlı, remarking its connection to Refs. [6,8].…”

“…Moreover, the commutator of a special conformal transformation and a supersymmetry generates a new fermionic symmetry: a conformal supersymmetry. Here, we skip cases with N = 1B and N = 2B with one R−symmetry as they are well explained in detail in [4]. We just remark that their superconformal generators obey the osp(1|2) and su(1, 1|1) algebras, respectively.…”

“…They become fully conformal invariant only after gauging a certain isometry group. For a full discussion on the gauging procedure in canonical formalism and the quantization of these models, as well as a more comprehensive list of references, please check the original paper [4].…”

“…Among our gauged superconformal sigma models with various numbers of supersymmetries, the N = 4B cases are particularly interesting, as they include a physically relevant subclass [4]. For α = 0, the model effectively describes an n-node Coulomb branch quiver quantum mechanics [5,6].…”