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10 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling

We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb{Z}$ N topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb{Z}$ N TQFT structure arises naturally from turning on a classical background field for a $\mathbb{Z}$ N 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to $\mathbb{Z}$ N TQFT, the non-perturbative expansion parameter is exp[-S I /N] = exp[-8π 2 /g 2 N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T 3 x $S^1_L$ can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $\mathbb{CP}$ 1 model, and mass gap for arbitrary θ in $\mathbb{CP}$ N-1 , N ≥ 3 on $\mathbb{R}$ 2 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Solving 3d gravity with Virasoro TQFT

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichmüller space of Riemann surfaces that we refer to as “Virasoro TQFT”. This TQFT is similar, but importantly not equivalent, to SL(2, \mathbb{R} ℝ ) Chern-Simons theory. This sharpens the folklore that 3d gravity is related to SL(2, \mathbb{R} ℝ ) Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level. Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity. In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge. Mathematically, the relation leads to many nontrivial conjectures for hyperbolic 3-manifolds, Virasoro conformal blocks and crossing kernels.

Collier, Scott↗
DOE OSTI2024

3d gravity from Virasoro TQFT: Holography, wormholes and knots

We further develop the description of three-dimensional quantum gravity with negative cosmological constant in terms of Virasoro TQFT formulated in our previous paper [SciPost Phys. 15, 151 (2023)]. We compare the partition functions computed in the Virasoro TQFT formalism to the semiclassical evaluation of Euclidean gravity partition functions. This matching is highly non-trivial, but can be checked directly in some examples. We then showcase the formalism in action, by computing the gravity partition functions of many relevant topologies. For holographic applications, we focus on the partition functions of Euclidean multi-boundary wormholes with three-punctured spheres as boundaries. This precisely quantifies the higher moments of the structure constants in the proposed ensemble boundary dual and subjects the proposal to thorough checks. Finally, we investigate in detail the example of the figure eight knot complement as a hyperbolic 3-manifold. We show that the Virasoro TQFT partition function is identical to the partition function computed in Teichmüller theory, thus giving strong evidence for the equivalence of these TQFTs. We also show how to produce a large class of manifolds via Dehn surgery on the figure eight knot.

Collier, Scott (ORCID:0000000286476653)↗
DOE OSTI2023

Non-Semisimple TQFT's and BPS q -Series

We propose and in some cases prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic q. Both types of invariants are labeled by extra data which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows to study (and perhaps even to formulate) q-series invariants labeled by spin c structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.

3-manifold invariants↗
DOE OSTI2026

Proliferation transitions from a topological phase in 2+1 dimensions

We consider phase transitions out of a general topological phase in 2+1 dimensions. We assume that the transition is triggered by a single Abelian anyon, which becomes light near the transition and whose worldlines proliferate after the transition. (This proliferation is often referred to as “condensation.”) We describe the transition using a continuum field theory obtained by coupling the corresponding topological quantum field theory (TQFT) to a single complex scalar field associated with this anyon. With these assumptions, we find the most general relativistic field theory for such a transition. Even though for a given TQFT and a choice of anyon, there are infinitely many such field theories, the transition theory depends on only a single additional integer parameter. We analyze all these theories, their global symmetries, and their phases. In generic cases, the theory after the transition can be related to the original one via an Abelian hierarchy construction. In special cases, the theory after the transition is gapless, and with a particular deformation, it is related to the original TQFT by gauging an anomaly-free one-form global symmetry. We also explore the enrichment of this setup by a global U⁡(1) symmetry. In some cases, enriching the original TQFT is incompatible with the full transition theory. Lastly, we demonstrate our construction with many specific examples.

Anyons↗
DOE OSTI2023

Decorated TQFTs and their Hilbert spaces

We discuss topological quantum field theories that compute topological invariants which depend on additional structures (or decorations) on three-manifolds. The q-series invariant $\hat{Z}$(q) proposed by Gukov, Pei, Putrov, and Vafa is an example of such an invariant. We describe how to obtain these decorated invariants by cutting and gluing and make a proposal for Hilbert spaces that are assigned to two-dimensional surfaces in the $\hat{Z}$-TQFT.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Open-closed 3d gravity as a random ensemble

We investigate an ensemble of boundary CFTs within the framework of a tensor model recently constructed to model 3d quantum gravity. The incorporation of CFT borders introduces new elements to the gravity theory. In particular, it leads to an open-closed extension of Virasoro TQFT, which in the classical limit gives rise to 3d gravity with tensionful end-of-the-world branes. It also provides predictions for off-shell manifolds with bordered asymptotic boundaries, such as the annulus wormhole. As an application, we construct a purely open variant of the tensor model to study a purely open bootstrap problem in the context of CFT triangulation. We also briefly discuss the extension to non-orientable CFTs.

AdS-CFT correspondence↗
DOE OSTI2024

The metamorphosis of semi-classical mechanisms of confinement: from monopoles on ℝ 3 × S 1 to center-vortices on ℝ 2 × T 2

There are two distinct regimes of Yang-Mills theory where we can demonstrate confinement, the existence of a mass gap, and the multi-branch structure of the effective potential as a function of the theta angle using a reliable semi-classical calculation. The two regimes are deformed Yang-Mills theory on ℝ 3 × S 1 , and Yang-Mills theory on ℝ 2 × T 2 where the torus is threaded by a ’t Hooft flux. The weak coupling regime is ensured by the small size of the circle or torus. In the first case the confinement mechanism is related to self-dual monopoles, whereas in the second case self-dual center-vortices play a crucial role. These two topological objects are distinct. In particular, they have different mutual statistics with Wilson loops. On the other hand, they carry the same topological charge and action. We consider the theory on ℝ × T 2 × S 1 and extrapolate both the monopole and vortex regimes to a quantum mechanical domain, where a cross-over takes place. Both sides of the cross-over are described by a deformed ℤ N TQFT. On ℝ 2 × S 1 × S 1 , we derive an effective field theory (EFT) of vortices from the EFT of monopoles in the presence of a ’t Hooft flux. This construction is based on a two-stage Higgs mechanism, reducing SU(N) to U(1) N−1 in 3d first, followed by reduction to a ℤ N EFT in 2d in the second step. This result shows how monopoles transmute into center-vortices, and suggests adiabatic continuity between the two confinement mechanisms. The basic mechanism is flux fractionalization: the magnetic flux of the monopoles splits up and is collimated in such a way that 2d Wilson loops detect it as a center vortex.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

3d TQFTs from Argyres–Douglas theories

We construct a new class of three-dimensional topological quantum field theories (3d TQFTs) by considering generalized Argyres–Douglas theories on S 1 × M 3 with a non-trivial holonomy of a discrete global symmetry along the S 1 . For the minimal choice of the holonomy, the resulting 3d TQFTs are non-unitary and semisimple, thus distinguishing themselves from theories of Chern–Simons and Rozansky–Witten types respectively. Changing the holonomy performs a Galois transformation on the TQFT, which can sometimes give rise to more familiar unitary theories such as the ${\left({G}_{2}\right)}_{1}$ and ${\left({F}_{4}\right)}_{1}$ Chern–Simons theories. Our construction is based on an intriguing relation between topologically twisted partition functions, wild Hitchin characters, and chiral algebras which, when combined together, relate Coulomb branch and Higgs branch data of the same 4d $\mathcal{N}=2$ theory. Finally, we test our proposal by applying localization techniques to the conjectural $\mathcal{N}=1$ UV Lagrangian descriptions of the (A 1 , A 2 ), (A 1 , A 3 ) and (A 1 , D 3 ) theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Discrete theta angles, symmetries and anomalies

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d 4 d QCD with SU(N),SU(N)/\mathbb{Z}_k S U ( N ) , S U ( N ) / ℤ k or SO(N) S O ( N ) gauge groups as well as various 3d 3 d and 2d 2 d gauge theories.

Hsin, Po-Shen↗