2D Field Theories Research Articles

BMS modular covariance and structure constants

Two-dimensional (2d) field theories invariant under the Bondi-Metzner-Sachs algebra, or 2d BMSFTs in short, are putative holographic duals of Einstein gravity in 3d asymptotically flat spacetimes. When defined on a torus, these field theories come equipped with a modified modular structure. We use the modular covariance of the BMS torus two-point function to develop formulae for different three-point structure constants of the field theory. These structure constants indicate that BMSFTs follow the eigenstate thermalization hypothesis, albeit with some interesting changes to usual 2d CFTs. The singularity structures of the structure constants contain information on perturbations of cosmological horizons in 3d asymptotically flat spacetimes, which we show can also be obtained as a limit of BTZ quasinormal modes.

Timelike entanglement entropy

We define a new complex-valued measure of information called the timelike entanglement entropy (EE) which in the boundary theory can be viewed as a Wick rotation that changes a spacelike boundary subregion to a timelike one. An explicit definition of the timelike EE in 2d field theories is provided followed by numerical computations which agree with the analytic continuation of the replica method for CFTs. We argue that timelike EE should be correctly interpreted as another measure previously considered, the pseudo entropy, which is the von Neumann entropy of a reduced transition matrix. Our results strongly imply that the imaginary part of the pseudo entropy describes an emergent time which generalizes the notion of an emergent space from quantum entanglement. For holographic systems we define the timelike EE as the total complex valued area of a particular stationary combination of both space and timelike extremal surfaces which are homologous to the boundary region. For the examples considered we find explicit matching of our optimization procedure and the careful implementation of the Wick rotation in the boundary CFT. We also make progress on higher dimensional generalizations and relations to holographic pseudo entropy in de Sitter space.

Simulation of a Transverse Flux Linear Induction Motor to Determine an Equivalent Circuit Using 3D Finite Element

This paper presents a Transverse Flux Linear Induction Motor prototype simulated with a 3D Finite Element tool. The main objective of the paper is to obtain an accurate method to construct an equivalent circuit that simulates the motor, using some specific parameters. The method has three steps. In the first step, we simulate two indirect tests to represent rotating induction machines, standstill and locked rotor tests. Using the test results, we define an equations system that incorporates the longitudinal end-effect. The system allows us to select specific parameters needed to build the equivalent circuit using six different configurations. In the second step, we classify the parameters in two groups: parameters from the primary and secondary parts. We test the primary part parameters defining the magnetizing inductance as a combination of the longitudinal and the transversal magnetizing inductance. To this end, the method analyses the first harmonic of the magnetic field wave along the air gap, which is located above the central teeth. Thus, it is possible to establish a difference between transversal and longitudinal components of the magnetic field density. The parameters of the secondary part will be compared using 2D Field Theory with a linear induction motor that operates with a transverse flux configuration. In the third step, the method analyses the selected parameters using a goodness factor, a dimensionless key performance indicator, specifically used to evaluate the behavior of linear induction motors and the specific parameters estimated for the equivalent circuit.

M5-branes probing flux backgrounds

We analyze the global symmetries and anomalies of 4d mathcal{N} = 1 field theories that arise from a stack of N M5-branes probing a class of flux backgrounds. These backgrounds consist of a resolved ℂ2/ℤk singularity fibered over a smooth Riemann surface of genus g ≥ 2, supported by a non-trivial G4-flux configuration labeled by a collection of 2(k − 1) flux quanta, {Ni}. For k = 2, this setup defines a non-trivial superconformal field theory (SCFT) in the IR, which is holographically dual to an explicit AdS5 solution first described by Gauntlett, Martelli, Sparks, and Waldram. The generalization to k ≥ 3 is hard to tackle directly within holography. Instead, in this paper we lay the groundwork for a systematic analysis of such a generalization by adopting anomaly inflow methods to identify continuous and discrete global symmetries of the 4d field theories. We also compute the ’t Hooft anomalies for continuous symmetries at leading order in the limit of large N, Ni.

The geometry of decoupling fields

We consider 4d field theories obtained by reducing the 6d (1,0) SCFT of N M5-branes probing a ℂ2/ℤk singularity on a Riemann surface with fluxes. We follow two different routes. On the one hand, we consider the integration of the anomaly polynomial of the parent 6d SCFT on the Riemann surface. On the other hand, we perform an anomaly inflow analysis directly from eleven dimensions, from a setup with M5-branes probing a resolved ℂ2/ℤk singularity fibered over the Riemann surface. By comparing the 4d anomaly polynomials, we provide a characterization of a class of modes that decouple along the RG flow from six to four dimensions, for generic N, k, and genus. These modes are identified with the flip fields encountered in the Lagrangian descriptions of these 4d models, when they are available. We show that such fields couple to operators originating from M2-branes wrapping the resolution cycles. This provides a geometric origin of flip fields. They interpolate between the 6d theory in the UV, where the M2-brane operators are projected out, and the 4d theory in the IR, where these M2-brane operators are part of the spectrum.

F‐theory and Dark Energy

AbstractMotivated by its potential use as a starting point for solving various cosmological constant problems, we study F‐theory compactified on the warped product where Y8 is a manifold, and the S3 factor is the target space of an Wess–Zumino–Witten (WZW) model at level N. Reduction to M‐theory exploits the abelian duality of this WZW model to an orbifold. In the large N limit, the untwisted sector is captured by 11D supergravity. The local dynamics of intersecting 7‐branes in the geometry is controlled by a Donaldson–Witten twisted gauge theory coupled to defects. At late times, the system is governed by a 1D quantum mechanics system with a ground state annihilated by two real supercharges, which in four dimensions would appear as “ supersymmetry” on a curved background. This leads to a cancellation of zero point energies in the 4D field theory but a split mass spectrum for superpartners of order specified by the IR and UV cutoffs of the model. This is suggestively close to the TeV scale in some scenarios. The classical 4D geometry has an intrinsic instability which can produce either a collapsing or expanding Universe, the latter providing a promising starting point for a number of cosmological scenarios. The resulting 1D quantum mechanics in the time direction also provides an appealing starting point for a more detailed study of quantum cosmology.

Chiral transport in strong fields from holography

Anomaly-induced transport phenomena in presence of strong external electromagnetic fields are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. Two complementary studies are reported. In the first one, we present results on the Ohmic conductivity, diffusion constant, chiral magnetic conductivity, and additional anomaly-induced transport coefficients as functions of external e/m fields. Next, gradient resummation in a constant background magnetic field is performed. All-order resummed constitutive relations are parameterised by four momenta-dependent transport coefficient functions (TCFs). A highlight of this part is a thorough study of non-dissipative chiral magnetic waves (CMW) in strong magnetic fields.

Gradient resummation for nonlinear chiral transport: an insight from holography

Nonlinear transport phenomena induced by chiral anomaly are explored within a 4D field theory defined holographically as U(1)_Vtimes U(1)_A Maxwell–Chern–Simons theory in Schwarzschild-AdS_5. In presence of weak constant background electromagnetic fields, the constitutive relations for vector and axial currents, resummed to all orders in the gradients of charge densities, are encoded in nine momenta-dependent transport coefficient functions (TCFs). These TCFs are first calculated analytically up to third order in gradient expansion, and then evaluated numerically beyond the hydrodynamic limit. Fourier transformed, the TCFs become memory functions. The memory function of the chiral magnetic effect (CME) is found to differ dramatically from the instantaneous response form of the original CME. Beyond hydrodynamic limit and when external magnetic field is larger than some critical value, the chiral magnetic wave (CMW) is discovered to possess a discrete spectrum of non-dissipative modes.

Nonlinear chiral transport from holography

Nonlinear transport phenomena induced by the chiral anomaly are explored within a 4D field theory defined holographically as U(1)V × U(1)A Maxwell-Chern-Simons theory in Schwarzschild-AdS5. First, in presence of external electromagnetic fields, a general form of vector and axial currents is derived. Then, within the gradient expansion up to third order, we analytically compute all (over 50) transport coefficients. A wealth of higher order (nonlinear) transport phenomena induced by chiral anomaly are found beyond the Chiral Magnetic and Chiral Separation Effects. Some of the higher order terms are relaxation time corrections to the lowest order nonlinear effects. The charge diffusion constant and dispersion relation of the Chiral Magnetic Wave are found to receive anomaly-induced non-linear corrections due to e/m background fields. Furthermore, there emerges a new gapless mode, which we refer to as Chiral Hall Density Wave, propagating along the background Poynting vector.

Generating hierarchies with Anderson localisation

We consider how the effect of Anderson localisation in a one-dimensional, disordered lattice can be applied to generate exponential hierarchies amongst the couplings of 4D field theories. This may have applications in the study of beyond the Standard Model physics; we give a proof-of-concept model for the generation of small neutrino masses.

The nuts and bolts of the BMS bootstrap

In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of crossing symmetry in 4-point functions that are constrained by symmetry. The BMS bootstrap equation is formulated and then analytic expressions for BMS blocks are constructed by looking at the limit of large central charges. These results are also applicable to 2d Galilean conformal field theories (CFTs) through the isomorphism between the BMS3 and 2d Galilean conformal algebras. We recover our previously obtained results in the non-relativistic limit of the corresponding ones in 2d relativistic CFTs. This provides a comprehensive check of our previous analysis. We also explore the chiral limit of BMS3 where the BMS algebra reduces to a single copy of the Virasoro algebra and show that our analysis is consistent with earlier work in this direction.

Flat holography: aspects of the dual field theory

Assuming the existence of a field theory in D dimensions dual to (D+1)-dimensional flat space, governed by the asymptotic symmetries of flat space, we make some preliminary remarks about the properties of this field theory. We review briefly some successes of the 3d bulk - 2d boundary case and then focus on the 4d bulk - 3d boundary example, where the symmetry in question is the infinite dimensional BMS4 algebra. We look at the constraints imposed by this symmetry on a 3d field theory by constructing highest weight representations of this algebra. We construct two and three point functions of BMS primary fields and surprisingly find that symmetries constrain these correlators to be identical to those of a 2d relativistic conformal field theory. We then go one dimension higher and construct prototypical examples of 4d field theories which are putative duals of 5d Minkowski spacetimes. These field theories are ultra-relativistic limits of electrodynamics and Yang-Mills theories which exhibit invariance under the conformal Carroll group in D=4. We explore the different sectors within these Carrollian gauge theories and investigate the symmetries of the equations of motion to find that an infinite ultra-relativistic conformal structure arises in each case.

Phase diagram of 4D field theories with chiral anomaly from holography

Within gauge/gravity duality, we study the class of four dimensional CFTs with chiral anomaly described by Einstein-Maxwell-Chern-Simons theory in five dimensions. In particular we determine the phase diagram at finite temperature, chemical potential and magnetic field. At high temperatures the solution is given by an electrically and magnetically charged AdS Reissner-Nordstroem black brane. For sufficiently large Chern-Simons coupling and at sufficiently low temperatures and small magnetic fields, we find a new phase with helical order, breaking translational invariance spontaneously. For the Chern-Simons couplings studied, the phase transition is second order with mean field exponents. Since the entropy density vanishes in the limit of zero temperature we are confident that this is the true ground state which is the holographic version of a chiral magnetic spiral.

Sigma models for genuinely non-geometric backgrounds

The existence of genuinely non-geometric backgrounds, i.e. ones without geometric dual, is an important question in string theory. In this paper we examine this question from a sigma model perspective. First we construct a particular class of Courant algebroids as protobialgebroids with all types of geometric and non-geometric fluxes. For such structures we apply the mathematical result that any Courant algebroid gives rise to a 3D topological sigma model of the AKSZ type and we discuss the corresponding 2D field theories. It is found that these models are always geometric, even when both 2-form and 2-vector fields are neither vanishing nor inverse of one another. Taking a further step, we suggest an extended class of 3D sigma models, whose world volume is embedded in phase space, which allow for genuinely non-geometric backgrounds. Adopting the doubled formalism such models can be related to double field theory, albeit from a world sheet perspective.

Gauge symmetries in 2D field theory

A simple algorithm is proposed for constructing generators of gauge symmetry as well as reducibility relations for arbitrary systems of field equations in two dimensions.

Multi-Matrix Models and Noncommutative Frobenius Algebras Obtained from Symmetric Groups and Brauer Algebras

It has been understood that correlation functions of multi-trace operators in ${\cal N}=4$ SYM can be neatly computed using the group algebra of symmetric groups or walled Brauer algebras. On the other hand such algebras have been known to construct 2D topological field theories (TFTs). After reviewing the construction of 2D TFTs based on symmetric groups, we construct 2D TFTs based on walled Brauer algebras. In the construction, the introduction of a dual basis manifests a similarity between the two theories. We next construct a class of 2D field theories whose physical operators have the same symmetry as multi-trace operators constructed from some matrices. Such field theories correspond to non-commutative Frobenius algebras. A matrix structure arises as a consequence of the noncommutativity. Correlation functions of the Gaussian complex multi-matrix models can be translated into correlation functions of the two-dimensional field theories.

AdS/CFT for accelerator physics

The crucial property of particle colliders is their ability to convert (e.g. electrical) energy into the mass of heavy particles. We have become used to the extremely low efficiency of this conversion and the severe limitations on the mass scale of heavy particles that can be reached. In view of this situation, it appears reasonable to ask whether a perfect conversion machine of this type (a perfect ``collider'') exists even in principle and whether there is a highest mass scale that can be reached by such a machine. It turns out that, with a number of assumptions, such a machine is conceivable in a world with a strongly coupled, approximately scale-invariant four-dimensional (4D) field theory with five-dimensional (5D) gravity dual. This machine can be realized as a 5D tower built on the IR brane (in Randall-Sundrum model language). Transporting mass to the tip of this tower is, under certain conditions, equivalent to producing heavy pointlike 4D particles. Hence, this can be thought of as a perfect ``collider.'' In the simple, ``pure Randall-Sundrum setting'' that we analyze, this machine can only reach a certain maximal energy scale, which falls as the gravity-dual of the 4D quantum field theory (QFT) approaches the strong coupling domain. On these grounds, one might expect that a no-go theorem (in the spirit of that of Carnot for the conversion of heat into work) exists for generic weakly coupled QFTs.

A minimally tuned composite Higgs model from an extra dimension

We construct and study the 5D realization of a composite Higgs model with minimal tuning. The Higgs is a (pseudo-)Goldstone boson from the spontaneous breaking of a global SO(5) symmetry to an SO(4) subgroup. The peculiarity of our construction lies in the specific choice of the SO(5) representations of the 5D fermions from which the Standard Model fields arise as chiral zero modes. This choice reduces the tuning of these models to the minimal model-independent value allowed by electroweak precision tests. We analyse the main differences between our 5D construction and other descriptions in terms of purely 4D field theories. 5D models are generally more constrained and show a generic difficulty in accommodating a light Higgs without reintroducing large corrections to the (S) over cap parameter. We propose a specific construction in which this tension can be, even though accidentally, relaxed. We discuss the spectrum of the top partners in the viable regions of parameter space and predict the existence of light exotic quarks, gamma, of charge 8/3 whose striking decay channel gamma -> W(+)W(+)W(+)b can lead to either exclusion or confirmation of the model in the near future.

SOFT WALL MODEL WITH INVERSE EXPONENTIAL PROFILE AS A MODEL FOR THE AXIAL AND PSEUDOSCALAR MESONS

According to the conjecture of the gauge/gravity duality, a strongly coupled 4D field theory may be described by a dual 5D theory which is a free field theory in the first approximation. The usual description of the axial-vector sector in the bottom–up AdS/QCD models includes, however, the quartic interaction with a bulk scalar field. A question arises, whether it is possible to describe some aspects of the chiral symmetry breaking (CSB) in a way more consistent with the original proposal, i.e. within a free 5D theory? We suggest that a natural candidate for this purpose is the soft wall (SW) model with inverse exponential profile.

Non-Abelian discrete gauge symmetries in 4d string models

We study the realization of non-Abelian discrete gauge symmetries in 4d field theory and string theory compactifications. The underlying structure generalizes the Abelian case, and follows from the interplay between gaugings of non-Abelian isometries of the scalar manifold and field identifications making axion-like fields periodic. We present several classes of string constructions realizing non-Abelian discrete gauge symmetries. In particular, compactifications with torsion homology classes, where non-Abelianity arises microscopically from the Hanany-Witten effect, or compactifications with non-Abelian discrete isometry groups, like twisted tori. We finally focus on the more interesting case of magnetized branes in toroidal compactifications and quotients thereof (and their heterotic and intersecting duals), in which the non-Abelian discrete gauge symmetries imply powerful selection rules for Yukawa couplings of charged matter fields. In particular, in MSSM-like models they correspond to discrete flavour symmetries constraining the quark and lepton mass matrices, as we show in specific examples.