An official website of the United States government
We develop representation theoretic techniques to construct three dimensional non-semisimple topological quantum field theories which model homologically truncated topological B-twists of abelian Gaiotto--Witten theory with linear matter. Our constructions are based on relative modular structures on the category of weight modules over an unrolled quantization of a Lie superalgebra. The Lie superalgebra, originally defined by Gaiotto and Witten, is associated to a complex symplectic representation of a metric abelian Lie algebra. The physical theories we model admit alternative realizations as Chern--Simons-Rozansky--Witten theories and supergroup Chern--Simons theories and include as particular examples global forms of gl(1,1)-Chern--Simons theory and toral Chern--Simons theory. Fundamental to our approach is the systematic incorporation of non-genuine line operators which source flat connections for the topological flavour symmetry of the theory.
more »
« less
Topological Gauge Actions on the Lattice as Overlap Fermion Determinants
Overlap fermion on the lattice has been shown to properly reproduce topological aspects of gauge fields. In this paper, we review the derivation of Overlap fermion formalism in a torus of three space-time dimensions. Using the formalism, we show how to use the Overlap fermion determinants in the massless and infinite mass limits to construct different continuum topological gauge actions, such as the level-k Chern–Simons action, “half-CS” term and the mixed Chern–Simons (BF) coupling, in a gauge-invariant lattice UV regulated manner. Taking special Abelian and non-Abelian background fields, we demonstrate numerically how the lattice formalism beautifully reproduces the continuum expectations, such as the flow of action under large gauge transformations.
more »
« less
- Award ID(s):
- 1913010
- PAR ID:
- 10334760
- Date Published:
- Journal Name:
- Universe
- Volume:
- 8
- Issue:
- 6
- ISSN:
- 2218-1997
- Page Range / eLocation ID:
- 332
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)A bstract We use radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. The final state is a coherent state while on the initial state the holonomy operator has zero eigenvalue. The latter choice encodes the constraint that the gauge fields must be regular everywhere inside the handlebody. By requiring that the only singularities of the gauge field inside the handlebody must be compatible with Wilson loop insertions, we find that the Wilson loop shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique state in the Hilbert space obtained from a Kähler quantization of the theory on the constant-radius Riemann surfaces. Radial quantization allows us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we show that our method reproduces the known partition function at genus one.more » « less
-
A bstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices : codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.more » « less
-
A bstract We undertake a general study of the boundary (or edge) modes that arise in gauge and gravitational theories defined on a space with boundary, either asymptotic or at finite distance, focusing on efficient techniques for computing the corresponding boundary action. Such actions capture all the dynamics of the system that are implied by its asymptotic symmetry group, such as correlation functions of the corresponding conserved currents. Working in the covariant phase space formalism, we develop a collection of approaches for isolating the boundary modes and their dynamics, and illustrate with various examples, notably AdS 3 gravity (with and without a gravitational Chern-Simons terms) subject to assorted boundary conditions.more » « less
-
We obtain the nonequilibrium condensate of the Chern Simons density induced by a misaligned homogeneous coherent axion field in linear response. The Chern-Simons dynamical susceptibility is simply related to the axion self-energy, a result that is valid to leading order in the axion coupling but to all orders in the couplings of the gauge fields to other fields within or beyond the standard model except the axion. The induced Chern-Simons density requires renormalization which is achieved by vacuum subtraction.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/universe8060332
