Three-dimensional Field Theory Research Articles

Phase transitions of magneticAdS4black holes with scalar hair

We determine the thermodynamic properties of a class of spherically symmetric and static black holes in AdS4 with magnetic charges and scalar hair. These black holes are solutions in 4d N=2 gauged supergravity that can arise from eleven-dimensional supergravity compactified on S^7. At zero temperature, they preserve supersymmetry and hence are stable. At non-zero temperatures, we explore in detail the canonical ensemble and stability of solutions and find a first order phase transition between small and large hairy black holes. The transition emerges as a liquid-gas phase transition in the dual three-dimensional field theory on R x S^2 with magnetic flux through S^2.

Scattering amplitudes in three-dimensional superconformal field theory

Recent progress in computation of loop amplitudes in three-dimensional superconformal models is reviewed.

Spontaneous Generation of Angular Momentum in Holographic Theories

The Schwarzschild black two-brane in four-dimensional anti-deSitter space is dual to a finite temperature state in three-dimensional conformal field theory. We show that the solution acquires a nonzero angular momentum density when a gravitational Chern-Simons coupling is turned on in the bulk, even though the solution is not modified. A similar phenomenon is found for the Reissner-Nordström black two-brane with axionic coupling to the gauge field. We discuss interpretation of this phenomenon from the point of view of the boundary three-dimensional conformal field theory.

Constraining conformal field theories with a higher spin symmetry

We study the constraints imposed by the existence of a single higher spin conserved current on a three-dimensional conformal field theory (CFT). A single higher spin conserved current implies the existence of an infinite number of higher spin conserved currents. The correlation functions of the stress tensor and the conserved currents are then shown to be equal to those of a free field theory. Namely a theory of N free bosons or free fermions. This is an extension of the Coleman–Mandula theorem to CFT’s, which do not have a conventional S-matrix. We also briefly discuss the case where the higher spin symmetries are ‘slightly’ broken.This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Higher spin theories and holography’.

Bicategories for Boundary Conditions and for Surface Defects in 3-d TFT

We analyze topological boundary conditions and topological surface defects in three-dimensional topological field theories of Reshetikhin-Turaev type based on arbitrary modular tensor categories. Boundary conditions are described by central functors that lift to trivializations in the Witt group of modular tensor categories. The bicategory of boundary conditions can be described through the bicategory of module categories over any such trivialization. A similar description is obtained for topological surface defects. Using string diagrams for bicategories we also establish a precise relation between special symmetric Frobenius algebras and Wilson lines involving special defects. We compare our results with previous work of Kapustin-Saulina and of Kitaev-Kong on boundary conditions and surface defects in abelian Chern-Simons theories and in Turaev-Viro type TFTs, respectively.

Constraining conformal field theories with a slightly broken higher spin symmetry

We consider three-dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large-N limit in the sense that the operators separate into single trace and multitrace and obey the usual large-N factorization properties. We assume that the spectrum of single trace operators is similar to the one that one obtains in the Vasiliev theories. Namely the only single trace operators are the higher spin currents plus an additional scalar. The anomalous dimensions of the higher spin currents are of the order 1/N. Using the slightly broken higher spin symmetry, we constrain the three-point functions of the theories to a leading order in N. We show that there are two families of solutions. One family can be realized as a theory of N fermions with an O(N) Chern–Simons gauge field, the other as an N bosons plus the Chern–Simons gauge field. The family of solutions is parametrized by the 't Hooft coupling. At special parity preserving points, we obtain the critical O(N) models: the Wilson–Fisher one and the Gross–Neveu one. Our analysis also fixes the on-shell three-point functions of Vasiliev's theory on AdS4 or dS4.

A non-renormalization theorem in gapped quantum field theory

We discuss the two-point functions of the U(1) current and energy-momentum tensor in certain gapped three-dimensional field theories, and show that the parity-odd part in both of these correlation functions is one-loop exact. In particular, we find a new and simplified derivation of the Coleman-Hill theorem that also clarifies several subtleties in the original argument. For the energy momentum tensor, our result means that the gravitational Chern-Simons term for the background metric does not receive quantum corrections

A crack in the conformal window

In {\cal N} = 2 superconformal three-dimensional field theory the R-symmetry is determined by locally maximizing the free energy F on the three-sphere. Using F-maximization, we study the {\cal N} = 2 supersymmetric U(N_c) gauge theory coupled to N_f pairs of fundamental and anti-fundamental superfields in the Veneziano large N_c limit, where x = N_f / N_c is kept fixed. This theory has a superconformal window 1 \leq x \leq \infty, while for x < 1 supersymmetry is broken. As we reduce x we find "a crack in the superconformal window" - a critical value x_c \approx 1.45 where the monopole operators reach the unitarity bound. To continue the theory to x < x_c we assume that the monopoles become free fields, leading to an accidental global symmetry. Using the Aharony dual description of the theory for x < x_c allows us to determine the R-charges and F for 1 \leq x < x_c. Adding a Chern-Simons term removes the transition at x_c. In these more general theories we study the scaling dimensions of meson operators as functions of x and \kappa = |k| / N_c. We find that there is an interesting transition in behavior at \kappa = 1.

On the refined counting of graphs on surfaces

Ribbon graphs embedded on a Riemann surface provide a useful way to describe the double-line Feynman diagrams of large N computations and a variety of other QFT correlator and scattering amplitude calculations, e.g. in MHV rules for scattering amplitudes, as well as in ordinary QED. Their counting is a special case of the counting of bi-partite embedded graphs. We review and extend relevant mathematical literature and present results on the counting of some infinite classes of bi-partite graphs. Permutation groups and representations as well as double cosets and quotients of graphs are useful mathematical tools. The counting results are refined according to data of physical relevance, such as the structure of the vertices, faces and genus of the embedded graph. These counting problems can be expressed in terms of observables in three-dimensional topological field theory with Sd gauge group which gives them a topological membrane interpretation.

Three-dimensional superconformal field theories, indices, and monopoles

We explain the recent progress in three-dimensional superconformal field theories based on the index for magnetic monopole operators and discuss applications to M2-branes and the AdS/CFT duality.

Exploring thermodynamic stability of the stalk fusion-intermediate with three-dimensional self-consistent field theory calculations

The prospects of compressible Self-Consistent Field (SCF) theory schemes for describing structures in amphiphilic membranes are illustrated by considering the thermodynamic stability of hourglass-shaped, hydrophobic connections (stalks) between apposed bilayers. The membranes are represented by a coarse-grained, solvent-free model. We represent the chain architecture by a Gaussian-thread representation of the chain architecture and capture the non-bonded interactions with a functional, which is of third-order in the densities of the hydrophilic and the hydrophobic segments. Using a three dimensional real-space scheme, we study the thermodynamic stability of the stalk with respect to two planar apposing bilayers as a function of membrane tension and molecular asymmetry. The structure and thermodynamics predicted by SCF theory agree very well with particle-based simulations, which include fluctuations. We discuss how the longer-range perturbations of the membrane induced by the stalk can affect thermodynamic properties.

Micellization of linear A-b-(B-alt-C)n multiblock terpolymers in A-selective solvents

We used three-dimensional self-consistent field theory to investigate the micellization behavior of A-b-(B-alt-C)n multiblock terpolymers in the presence of a solvent that is selective to the terminal A-block. In particular, we focused on the effects of the incompatibility parameter between B and C, χBC, and the composition of the solvophilic A-block, fA, on the formation of micelles from ABC triblock and A(BC)3 multiblock terpolymers, respectively. We observed a general trend that a segmented packing of B- and C-layers along the axial direction of the micelles is favored than the coaxial packing with the increasing of χBC or decreasing of fA. The separation of B and C blocks within a micelle leads to the formation of a variety of multicompartment micelle morphologies, such as core–shell–corona spherical micelles, hamburgers, and bump-surface micelles, in the ABC triblock copolymers. In the A(BC)3 multiblock terpolymers, we discovered more fascinating micelles by implementing the SCFT simulation than by the DPD simulation. Besides the BC-segmented worm-like micelles, which have been found in the DPD simulation work, concentric multilayer spheres and vesicles can be formed by the solvent-induced effect when the solvophilic A-block is a majority component. The SCFT method provides an efficient way to screen promising molecular architectures for the ability to self-assemble into technologically promising hierarchical structures.

Brane resolution through fibration

We consider p-branes with one or more circular directions fibered over the transverse space. The fibration, in conjunction with the transverse space having a blown-up cycle, enables these p-brane solutions to be completely regular. Some such circularly-wrapped D3-brane solutions describe flows from SU(N)^3 N=2 theory, F_0 theory, as well as an infinite family of superconformal quiver gauge theories, down to three-dimensional field theories. We discuss the operators that are turned on away from the UV fixed points. Similarly, there are wrapped M2-brane solutions which describe smooth flows from known three-dimensional supersymmetric Chern-Simons matter theories, such as ABJM theory. We also consider p-brane solutions on gravitational instantons, and discuss various ways in which U-duality can be applied to yield other non-singular solutions.

Refined checks and exact dualities in three dimensions

We discuss and provide nontrivial evidence for a large class of dualities in three-dimensional field theories with different gauge groups. We match the full partition functions of the dual phases for any value of the couplings to underpin our proposals. We focus on two classes of models. The first class, motivated by the AdS/CFT conjecture, consists of necklace U(N) quiver gauge theories with non chiral matter fields. We also consider orientifold projections and establish dualities among necklace quivers with alternating orthogonal and symplectic groups. The second class consists of theories with tensor matter fields with free theory duals. In most of these cases the R-symmetry mixes with IR accidental symmetries and we develop the prescription to include their contribution into the partition function and the extremization problem accordingly.

Holographic two-point functions for 4d log-gravity

We compute holographic one- and two-point functions of critical higher-curvature gravity in four dimensions. The two most important operators are the stress tensor and its logarithmic partner, sourced by ordinary massless and by logarithmic non-normalisable gravitons, respectively. In addition, the logarithmic gravitons source two ordinary operators, one with spin-one and one with spin-zero. The one-point function of the stress tensor vanishes for all Einstein solutions, but has a non-zero contribution from logarithmic gravitons. The two-point functions of all operators match the expectations from a three-dimensional logarithmic conformal field theory.

Comments on Chern-Simons contact terms in three dimensions

We study contact terms of conserved currents and the energy-momentum tensor in three-dimensional quantum field theory. They are associated with Chern-Simons terms for background fields. While the integer parts of these contact terms are ambiguous, their fractional parts are meaningful physical observables. In N=2 supersymmetric theories with a U(1)_R symmetry some of these observables lead to an anomaly. Moreover, they can be computed exactly using localization, leading to new tests of dualities.

Elucidating the Molecular Origin of Hydrolysis Energy of Pyrophosphate in Water.

The molecular origin of the energy produced by the ATP hydrolysis has been one of the long-standing fundamental issues. A classical view is that the negative hydrolysis free energy of ATP originates from intramolecular effects connected with the backbone P-O bond, so called "high-energy bond". On the other hand, it has also been recognized that solvation effects are essential in determining the hydrolysis free energy. Here, using the 3D-RISM-SCF (three-dimensional reference interaction site model self-consistent field) theory that integrates the ab initio quantum chemistry method and the statistical mechanical theory of liquids, we investigate the molecular origin of hydrolysis free energy of pyrophosphate, an ATP analogue, in water. We demonstrate that our theory quantitatively reproduces the experimental results without the use of empirical parameters. We clarify the crucial role of water in converting the hydrolysis free energy in the gas phase determined solely by intramolecular effects, which ranges from endothermic, thermoneutral, to highly exothermic depending on the charged state of pyrophosphate, into moderately exothermic in the aqueous phase irrespective of the charged state as observed in experimental data. We elucidate that this is brought about by different natures of solute-water interactions depending on the charged state of solute species: the hydration free energy of low-charged state is mainly subjected to short-range hydrogen-bonds, while that of high-charged state is dominated by long-range electrostatic interactions. We thus provide unambiguous evidence on the critical role of water in determining the ATP hydrolysis free energy.

A marker based kinematic method of identifying initial contact during gait for use in real-time visual feedback applications

This paper presents the analysis of the statistical size effect in steel structural elements using the stochastic finite element (FE) method. The three-dimensional random field theory is applied to simulate the uncertainty of a nonlinear material. The proposed approach, which combines the discrete random field describing the randomness of the material properties via Monte Carlo simulations, is used for computing the bearing capacity variability of the steel structures. In addition, the mapping interpolation method makes it possible to separate the random field mesh and FE model mesh. The three-dimensional random field for the material properties is established according to the yield strength with a lognormal distribution based on reasonable assumptions, and the corresponding random field parameters are studied. Finally, the results of experimental investigation and simulations are compared based on the tensile and bending tests, and they indicate that the statistical size effect cannot be overlooked in S235JR steel structural elements and that the use of stochastic FE in the analysis of the statistical size effect has tremendous potential.

Shape Dynamics and AdS/CFT

I present a semi-classical correspondence between three-dimensional euclidean conformal field theory and the large-volume dynamics of gravity with positive cosmological constant in 3+1 dimensions. The correspondence is based on a theory of gravity called Shape Dynamics, whose solutions are a subset of those of General Relativity, namely those that can be foliated with constant mean extrinsic curvature. Shape Dynamics makes it possible to solve exactly for all the local degrees of freedom, while in GR this is possible only approximately, within a derivative expansion, due to the non-linearity of the scalar constraint.

Entanglement entropy of 3-d conformal gauge theories with many flavors

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N F of bosonic and/or fermionic flavors to the first subleading order in 1/N F . We also calculate the exact free energies of the analogous chiral and non-chiral $ \mathcal{N} = 2 $ supersymmetric theories using localization, and find agreement with the 1/N F expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.