Three-dimensional Field Theory Research Articles

A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs

We introduce a novel class of two-dimensional non-unitary rational conformal field theories (RCFTs) whose modular data are identical to the generalized Haagerup-Izumi modular data. Via the bulk-boundary correspondence, they are related to the three-dimensional non-unitary Haagerup topological field theories, recently constructed by a topological twisting of three-dimensional N=4 rank-zero superconformal field theories (SCFTs), called S-fold SCFTs. We propose that, up to the overall factors, the half-indices of the rank-zero SCFTs give the explicit Nahm representation of four conformal characters of the RCFTs including the vacuum character. Using the theory of Bantay-Gannon, we can successfully complete them into the full admissible conformal characters of the RCFTs.

Holographic batteries

We study a three-dimensional holographic conformal field theory under the influence of a background electric field on a spacetime containing two black hole horizons. The electric background is fixed such that there is potential difference between the two boundary black holes, inducing a conserved current. By constructing the holographic duals to this setup, which are solutions to the Einstein-Maxwell equations with a negative cosmological constant in four dimensions, we calculate, to a fully nonlinear level, the conductivity of the conformal field theory in this background. Interestingly, we find that the conductivity depends nontrivially on the potential difference. The bulk solutions are flowing geometries containing black hole horizons which are non-Killing and have nonzero expansion. We find a novel property that the past boundary of the future horizon lies deep in the bulk and show this property remains present after small perturbations of the temperature difference of the boundary black holes. Published by the American Physical Society 2024

Non-Abelian currents bootstrap

We initiate the study of correlation functions of non-Abelian spin-1 conserved current in three-dimensional conformal field theories using numerical conformal bootstrap. We discuss the general framework and apply it to the particular cases of SU(N) and O(N) global symmetry. In both cases, we obtain general bounds on operator dimensions. In the large-N limit our bounds show features in correspondence of the expected position of fermionic QED3 in three dimensions, as well as other interesting theories. By imposing gaps inspired by the spectrum of QED3 at large-N, we manage to restrict the plane of certain operator dimensions to a small island, where QED3 must live.

Three-Dimensional Topological Field Theories and Nonunitary Minimal Models.

We find an intriguing relation between a class of three-dimensional nonunitary topological field theories (TFTs) and Virasoro minimal models M(2,2r+3) with r≥1. The TFTs are constructed by topologically twisting 3D N=4 superconformal field theories (SCFTs) of rank-0, i.e., having zero-dimensional Coulomb and Higgs branches. We present ultraviolet (UV) field theory descriptions of the SCFTs with manifest N=2 supersymmetry, which we argue is enhanced to N=4 in the infrared. From the UV description, we compute various partition functions of the TFTs and reproduce some basic properties of the minimal models, such as their characters and modular matrices. We expect more general correspondence between topologically twisted 3d N=4 rank-0 SCFTs and 2D nonunitary rational conformal field theories.

Solvent Distribution Effects on Quantum Chemical Calculations with Quantum Computers.

We present a combination of three-dimensional reference interaction site model self-consistent field (3D-RISM-SCF) theory and the variational quantum eigensolver (VQE) to consider the solvent distribution effects within the framework of quantum-classical hybrid computing. The present method, 3D-RISM-VQE, does not include any statistical errors from the solvent configuration sampling owing to the analytical treatment of the statistical solvent distribution. We apply 3D-RISM-VQE to compute the spatial distribution functions of solvent water around a water molecule, the potential and Helmholtz energy curves of NaCl, and to analyze the Helmholtz energy component and related properties of H2O and NH4+. Moreover, we utilize 3D-RISM-VQE to analyze the extent to which solvent effects alter the efficiency of quantum calculations compared with calculations in the gas phase using the L1-norms of molecular electronic Hamiltonians. Our results demonstrate that the efficiency of quantum chemical calculations on a quantum computer in solution is virtually the same as that in the gas phase.

Holographic RG flows from four-dimensional N = 2 gauged supergravities

In quantum field theories, the examination of particle interactions is facilitated through the application of Feynman diagrams. The computation of loop Feynman diagrams often yields divergent or infinite values. To tackle this issue, a method known as renormalization is employed, which entails the removal of these infinities. The phenomenon of a physical system undergoing changes under different scales gives rise to a concept referred to as the renormalization group. Certain renormalization group trajectories, denoted as RG flows, describe transformations of a conformal field theory (CFT) into other conformal or non-conformal theories. These transformations result in deformations of a UV conformal fixed point into another fixed point or into a non-conformal phase within the infrared (IR) regime. In this study, we investigate holographic RG flows originating from N = 2 gauged supergravity with an SO(2) × SO(6) gauge group. These solutions delineate RG flows from the N = 2 CFT to a three-dimensional non-conformal field theory driven by mass deformations. This transformation is elucidated through the AdS/CFT correspondence, also known as AdS/CFT holography.

A G-Equivariant String-Net Construction

We develop a string-net construction for the (2,1)-dimensional part of a G-equivariant three-dimensional topological field theory based on a G-graded spherical fusion category. In this construction, a G-equivariant generalization of the Ptolemy groupoid enters. We compute the associated cylinder categories and show that, as expected, the model is closely related to the G-equivariant Turaev–Viro theory.

Supersymmetric phases of AdS4/CFT3

We exhibit an infinite family of supersymmetric phases in the three-dimensional ABJM superconformal field theory and the dual asymptotically AdS4 gravity. They are interpreted as partially deconfined phases which generalize the confined/pure AdS phase and deconfined/supersymmetric black hole phase. Our analysis involves finding a family of saddle-points of the superconformal index labelled by rational points (equivalently, roots of unity), separately in the bulk and boundary theories. In the ABJM theory we calculate the free energy of each saddle by the large-N asymptotic expansion of the superconformal index to all orders in perturbation theory near the saddle-point. We find that this expansion terminates at finite order. In the gravitational theory we show that there is a corresponding family of solutions, constructed by orbifolding the eleven-dimensional uplift of the supersymmetric black hole. The on-shell gravitational action of each orbifold agrees with the free energy of the corresponding saddle in the SCFT. We find that there are two saddles in the ABJM theory with the same entropy as the supersymmetric black hole, corresponding to the two primitive fourth-roots of unity, which causes macroscopic oscillations in the microcanonical index.

D4-branes wrapped on a topological disk

Employing the method applied to M5-branes recently by Bah, Bonetti, Minasian and Nardoni, we study D4-branes wrapped on a disk with a non-trivial holonomy at the boundary. In F (4) gauged supergravity in six dimensions, we find supersymmetric AdS4 solutions and uplift the solutions to massive type IIA supergravity. We calculate the holographic free energy of dual three-dimensional superconformal field theories.

Accelerating Cosmology from a Holographic Wormhole.

We consider cosmological models in which the cosmology is related via analytic continuation to a Euclidean asymptotically AdS planar wormhole geometry defined holographically via a pair of three-dimensional Euclidean conformal field theories (CFTs). We argue that these models can generically give rise to an accelerating phase for the cosmology due to the potential energy of scalar fields associated with relevant scalar operators in the CFT. We explain how cosmological observables are related to observables in the wormhole spacetime and argue that this leads to a novel perspective on naturalness puzzles in cosmology.

Continuous generalized symmetries in three dimensions

We present a class of three-dimensional quantum field theories whose ordinary global symmetries mix with higher-form symmetries to form a continuous 2-group. All these models can be obtained by performing a gauging procedure in a parent theory revealing a ’t Hooft anomaly in the space of coupling constants when suitable compact scalar background fields are activated. Furthermore, the gauging procedure also implies that our main example has infinitely many non-invertible global symmetries. These can be obtained by dressing the continuous symmetry operators with topological quantum field theories. Finally, we comment on the holographic realization of both 2-group global symmetries and non-invertible symmetries discussed here by introducing a corresponding four-dimensional bulk description in terms of dynamical gauge fields.

Three-point functions of conserved currents in 3D CFT: General formalism for arbitrary spins

We analyse the general structure of the three-point functions involving conserved bosonic and fermionic higher-spin currents in three-dimensional conformal field theory. Using the constraints of conformal symmetry and conservation equations, we use a computational formalism to analyse the general structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where $J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The calculations are completely automated for any chosen spins and are limited only by computer power. We find that the correlation function is in general fixed up to two independent even structures, and one odd structure, subject to a set of triangle inequalities. We also analyse the structure of three-point functions involving higher-spin currents and fundamental scalars and spinors.

Domain Walls Between 3d Phases of Reshetikhin–Turaev TQFTs

We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin–Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we present an explicit and computable construction of such defects. It specialises to the construction in Carqueville et al. (Geom Topol 23:781–864, 2019. https://doi.org/10.2140/gt.2019.23.781. arXiv:1705.06085) if all 3-strata are labelled by the same topological field theory. We compare the results to the model-independent analysis in Fuchs et al. (Commun Math Phys 321:543–575, 2013. https://doi.org/10.1007/s00220-013-1723-0. arXiv:1203.4568) and find agreement.

Anyonic correlation functions in Chern-Simons matter theories

Using a novel relation between the parity-even and -odd parts of a correlator, we show that the three-point function of conserved or weakly broken currents in three-dimensional conformal field theory (CFT) can be obtained from just the free fermion (FF) or the free boson (FB) theory. In the special case of large $N$ Chern-Simons matter theories, we obtain the correlator in terms of a coupling constant dependent ``anyonic phase'' factor. This anyonic phase factor was previously obtained in the $2\ensuremath{\rightarrow}2$ exact S-matrix result and is consistent with strong-weak duality. By varying the coupling constant, the CFT correlator interpolates nicely between the same in the FF and FB theories.

Penrose limit of MNa solution and spin chains in three-dimensional field theories

In three dimensions, a theory with spontaneous breaking of supersymmetry was described holographically by the Maldacena-Nastase (MNa) solution. We revisit the issue of its Penrose limit, and compare the resulting pp wave and its string eigenstates to a sector of the theory on 5-branes reduced on S3, and a spin chain-like system. We obtain many of the features of the pp wave analysis, but a complete matching still eludes us. We suggest possible explanations for the resulting partial mismatch, and compare against other spin chains for 3-dimensional field theories with gravity duals.

Holographic evidence for nonsupersymmetric conformal manifolds

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

Implementation of solvent polarization in three-dimensional reference interaction-site model self-consistent field theory

The three-dimensional reference interaction-site model self-consistent field (3D-RISM-SCF) theory is an electronic structure theory of solvated molecules, which can handle the electronic polarization of the solute molecule induced by the interaction with the solvent, whereas the electronic polarization of solvent molecules is ignored. Here, the solvent-polarizable model is implemented to take into account the electronic polarization of solvent molecules. It is applied to the water molecule in an aqueous solution and the p-nitroaniline molecule in an aqueous solution, and the effects of the solvent polarization on the properties of these solutes are demonstrated.

Cosmology from confinement?

We describe a class of holographic models that may describe the physics of certain four-dimensional big-bang/big-crunch cosmologies. The construction involves a pair of 3D Euclidean holographic CFTs each on a homogeneous and isotropic space M coupled at either end of an interval ℐ to a Euclidean 4D CFT on M × ℐ with many fewer local degrees of freedom. We argue that in some cases, when the size of M is much greater than the length of ℐ, the theory flows to a confining three-dimensional field theory on M in the infrared, and this is reflected in the dual description by the asymptotically AdS spacetimes dual to the two 3D CFTs joining up in the IR to give a Euclidean wormhole. The Euclidean construction can be reinterpreted as generating a state of the Lorentzian 4D CFT on M × time whose dual includes the physics of a big-bang/big-crunch cosmology. When M is ℝ3, we can alternatively analytically continue one of the ℝ3 directions to get an eternally traversable four-dimensional planar wormhole. We suggest explicit microscopic examples where the 4D CFT is mathcal{N} = 4 SYM theory and the 3D CFTs are superconformal field theories with opposite orientation. In this case, the two geometries dual to the pair of 3D SCFTs can be understood as a geometrical version of a brane-antibrane pair, and the tendency of the geometries to connect up is related to the standard instability of brane-antibrane systems.

N=4 supersymmetric Yang-Mills thermodynamics from effective field theory

The free energy density of $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions is derived through second order in the 't Hooft coupling $\ensuremath{\lambda}$ at finite temperature using effective-field theory methods. The contributions to the free energy density at this order come from the hard scale $T$ and the soft scale $\sqrt{\ensuremath{\lambda}}T$. The effects of the scale $T$ are encoded in the coefficients of an effective three-dimensional field theory that is obtained by dimensional reduction at finite temperature. The effects of the electric scale $\sqrt{\ensuremath{\lambda}}T$ are taken into account by perturbative calculations in the effective theory.

Finding AdS5\xd7 S5 in 2+1 dimensional SCFT physics

We study solutions of type IIB string theory dual to mathcal{N} = 4 supersymmetric Yang-Mills theory on half of ℝ3,1 coupled to holographic three-dimensional superconformal field theories (SCFTs) at the edge of this half-space. The dual geometries are asymptotically AdS5×S5 with boundary geometry ℝ2,1×ℝ+, with a geometrical end-of-the-world (ETW) brane cutting off the other half of the asymptotic region of the would-be Poincaré AdS5×S5. We show that by choosing the 3D SCFT appropriately, this ETW brane can be pushed arbitrarily far towards the missing asymptotic region, recovering the “missing” half of Poincaré AdS5×S5. We also show that there are 3D SCFTs whose dual includes a wedge of Poincaré AdS5×S5 with an angle arbitrarily close to π, with geometrical ETW branes on either side.