A bstract We develop an approach to the study of Coulomb branch operators in 3D $$ \mathcal{N} $$ N = 4 gauge theories and the associated quantization structure of their Coulomb branches. This structure is encoded in a one-dimensional TQFT subsector of the full 3D theory, which we describe by combining several techniques and ideas. The answer takes the form of an associative and noncommutative star product algebra on the Coulomb branch. For “good” and “ugly” theories (according to the Gaiotto-Witten classification), we also exhibit a trace map on this algebra, which allows for the computation of correlation functions and, in particular, guarantees that the star product satisfies a truncation condition. This work extends previous work on abelian theories to the non-abelian case by quantifying the monopole bubbling that describes screening of GNO boundary conditions. In our approach, monopole bubbling is determined from the algebraic consistency of the OPE. This also yields a physical proof of the Bullimore-Dimofte-Gaiotto abelianization description of the Coulomb branch.
more »
« less
Spectral action in matrix form
Abstract Quantization of the noncommutative geometric spectral action has so far been performed on the final component form of the action where all traces over the Dirac matrices and symmetry algebra are carried out. In this work, in order to preserve the noncommutative geometric structure of the formalism, we derive the quantization rules for propagators and vertices in matrix form. We show that the results in the case of a product of a four-dimensional Euclidean manifold by a finite space, could be cast in the form of that of a Yang–Mills theory. We illustrate the procedure for the toy electroweak model.
more »
« less
- Award ID(s):
- 1912998
- NSF-PAR ID:
- 10274354
- Date Published:
- Journal Name:
- The European Physical Journal C
- Volume:
- 80
- Issue:
- 11
- ISSN:
- 1434-6044
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
The quantization of pure 3D gravity with Dirichlet boundaryconditions on a finite boundary is of interest both as a model ofquantum gravity in which one can compute quantities which are ``morelocal" than S-matrices or asymptotic boundary correlators, and forits proposed holographic duality to T\overline{T} T T ¯ -deformedCFTs. In this work we apply covariant phase space methods to deduce thePoisson bracket algebra of boundary observables. The result is aone-parameter nonlinear deformation of the usual Virasoro algebra ofasymptotically AdS _3 3 gravity. This algebra should be obeyed by the stress tensor in any T\overline{T} T T ¯ -deformedholographic CFT. We next initiate quantization of this system within thegeneral framework of coadjoint orbits, obtaining — in perturbationtheory — a deformed version of the Alekseev-Shatashvili symplectic formand its associated geometric action. The resulting energy spectrum isconsistent with the expected spectrum of T\overline{T} T T ¯ -deformedtheories, although we only carry out the explicit comparison to \mathcal{O}(1/\sqrt{c}) 𝒪 ( 1 / c ) in the 1/c 1 / c expansion.more » « less
-
Abstract We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in general noncommutativity yields a canonical time evolution, while at the same time allowing for the coexistence of discrete and continuous variables. The spectral approach to geometry is then explained to encompass two natural ingredients: the line element and the algebra. The relation between these two is dictated by so-called higher Heisenberg relations, from which both spin geometry and non-abelian gauge theory emerges. Our exposition indicates some of the applications in physics, including Pati–Salam unification beyond the Standard Model, the criticality of dimension 4, second quantization and entropy.more » « less
-
more » « less
A<sc>bstract</sc> We employ semiclassical quantization to calculate spectrum of quantum KdV charges in the limit of large central charge
c . Classically, KdV chargesQ 2n− 1generate completely integrable dynamics on the co-adjoint orbit of the Virasoro algebra. They can be expressed in terms of action variablesI k , e.g. as a power series expansion. Quantum-mechanically this series becomes the expansion in 1/c , while action variables become integer-valued quantum numbersn i . Crucially, classical expression, which is homogeneous inI k , acquires quantum corrections that include terms of subleading powers inn k . At first two non-trivial orders in 1/c expansion these “quantum” terms can be fixed from the analytic form ofQ 2n− 1acting on the primary states. In this way we find explicit expression for the spectrum ofQ 2n− 1up to first three orders in 1/c expansion. We apply this result to study thermal expectation values ofQ 2n− 1and free energy of the KdV Generalized Gibbs Ensemble. -
We consider a model of noncommutative gravity that is based on a spacetime with broken local SO(2,3) ☆ symmetry. We show that the torsion-free version of this model is contained within the framework of the Lorentz-violating Standard-Model Extension (SME). We analyze in detail the relation between the torsion-free, quadratic limits of the broken SO(2,3) ☆ model and the Standard-Model Extension. As part of the analysis, we construct the relevant geometric quantities to quadratic order in the metric perturbation around a flat background.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1140/epjc/s10052-020-08618-z
