4D Theory Research Articles

Kaluza-Klein gravitons at LHC2

In this work we study constraints from new searches for heavy particles at the LHC on the allowed masses and couplings of a KK Graviton in a holographic composite Higgs model. Keeping new electroweak states heavy such that electroweak precision tests are satisfied, we control the mass of the lightest KK graviton using a brane kinetic term. With this we study KK graviton masses from 0.5-3 TeV. In our analysis we also employ Little Randall-Sundrum (RS) Models, characterised by a lower UV scale in the 5D model which in turn implies modified couplings to massless bulk fields. Viewing this scenario as a strongly coupled 4D theory with a composite Higgs boson, the KK graviton is interpreted as a composite spin-2 state and the varying UV scale corresponds to a varying intermediate scale between the cutoff of the low energy effective theory and the Planck scale. We find that KK gravitons with masses in the range 0.5-3 TeV are compatible with current collider constraints, where the most promising channels for detecting these states are the di-photon and ZZ channels. A detection is more likely in the little RS models, in which the dual gauge theory has a larger number of colours than in traditional RS models.

Fermions in Two Dimensions: Scattering and Many-Body Properties

Ultracold atomic Fermi gases in two-dimensions (2D) are an increasingly popular topic of research. The interaction strength between spin-up and spin-down particles in two-component Fermi gases can be tuned in experiments, allowing for a strongly interacting regime where the gas properties are yet to be fully understood. We have probed this regime for 2D Fermi gases by performing T=0 ab initio diffusion Monte Carlo calculations. The many-body dynamics are largely dependent on the two-body interactions, therefore we start with an in-depth look at scattering theory in 2D. We show the partial-wave expansion and its relation to the scattering length and effective range. Then we discuss our numerical methods for determining these scattering parameters. We close out this discussion by illustrating the details of bound states in 2D. Transitioning to the many-body system, we use variationally optimized wave functions to calculate ground-state properties of the gas over a range of interaction strengths. We show results for the energy per particle and parametrize an equation of state. We then proceed to determine the chemical potential for the strongly interacting gas.

Macdonald index and chiral algebra

For any 4d mathcal{N} = 2 SCFT, there is a subsector described by a 2d chiral algebra. The vacuum character of the chiral algebra reproduces the Schur index of the corresponding 4d theory. The Macdonald index counts the same set of operators as the Schur index, but the former has one more fugacity than the latter. We conjecture a prescription to obtain the Macdonald index from the chiral algebra. The vacuum module admits a filtration, from which we construct an associated graded vector space. From this grading, we conjecture a notion of refined character for the vacuum module of a chiral algebra, which reproduces the Macdonald index. We test this prescription for the Argyres-Douglas theories of type (A1, A2n) and (A1, D2n+1) where the chiral algebras are given by Virasoro and widehat{mathfrak{su}}(2) affine Kac-Moody algebra. When the chiral algebra has more than one family of generators, our prescription requires a knowledge of the generators from the 4d.

Solving the Schwarzian via the conformal bootstrap

We obtain exact expressions for a general class of correlation functions in the 1D quantum mechanical model described by the Schwarzian action, that arises as the low energy limit of the SYK model. The answer takes the form of an integral of a momentum space amplitude obtained via a simple set of diagrammatic rules. The derivation relies on the precise equivalence between the 1D Schwarzian theory and a suitable large c limit of 2D Virasoro CFT. The mapping from the 1D to the 2D theory is similar to the construction of kinematic space. We also compute the out-of-time ordered four point function. The momentum space amplitude in this case contains an extra factor in the form of a crossing kernel, or R-matrix, given by a 6j-symbol of SU(1,1). We argue that the R-matrix describes the gravitational scattering amplitude near the horizon of an AdS2 black hole. Finally, we discuss the generalization of some of our results to mathcal{N}=1 and mathcal{N}=2 supersymmetric Schwarzian QM.

2D CFT blocks for the 4D class {mathcal{S}}_k theories

This is the first in a series of papers on the search for the 2D CFT description of a large class of 4D mathcal{N}=1 gauge theories. Here, we identify the 2D CFT symmetry algebra and its representations, namely the conformal blocks of the Virasoro/W-algebra, that underlie the 2D theory and reproduce the Seiberg-Witten curves of the mathcal{N}=1 gauge theories. We find that the blocks corresponding to the SU(N) {mathcal{S}}_k gauge theories involve fields in certain non-unitary representations of the WkN algebra. These conformal blocks give a prediction for the instanton partition functions of the 4D mathcal{N}=1 SCFTs of class {mathcal{S}}_k .

Unitarity problems in 3D gravity theories

We revisit the problem of the bulk-boundary unitarity clash in 2 + 1 dimensional gravity theories, which has been an obstacle in providing a viable dual two-dimensional conformal field theory for bulk gravity in anti-de Sitter (AdS) spacetime. Chiral gravity, which is a particular limit of cosmological topologically massive gravity (TMG), suffers from pertur- bative log-modes with negative energies inducing a non-unitary logarithmic boundary field theory. We show here that any f(R) extension of TMG does not improve the situation. We also study the perturbative modes in the metric formulation of minimal massive gravity- originally constructed in a first-order formulation-and find that the massive mode has again negative energy except in the chiral limit. We comment on this issue and also discuss a possible solution to the problem of negative energy modes. In any of these theories, the infinitesimal dangerous deformations might not be integrable to full solutions; this suggests a linearization instability of AdS spacetime in the direction of the perturbative log-modes.

A Chern-Simons pandemic

In this paper we study the consistency of generalized global symmetries in theories of quantum gravity, in particular string theory. Such global symmetries arise in theories with (p + 1)-form gauge fields, and for spacetime dimension d ≤ p + 3 there are obstructions to their breaking even by quantum effects of charged objects. In 4d theories with a 2-form gauge field (or with an axion scalar), these fields endow Schwarzschild black holes with quantum hair, a global charge leading to usual trouble with remnants. We describe precise mechanisms, and examples from string compactifications and holographic pairs, in which these problems are evaded by either gauging or breaking the global symmetry, via (suitable versions of) Stuckelberg or 4-form couplings. We argue that even in the absence of such couplings, the generic solution in string theory is the breaking of the global symmetries by cubic Chern-Simons terms involving different antisymmetric tensor fields. We conjecture that any theory with (standard or higher-degree antisymmetric tensor) gauge fields is in the Swampland unless its effective action includes such Chern-Simons terms. This conjecture implies that many familiar theories, like QED (even including the charged particles required by the Weak Gravity Conjecture) or mathcal{N}=8 supergravity in four dimensions, are inconsistent in quantum gravity unless they are completed by these Chern-Simons terms.

General relativity from three-forms in seven dimensions

We consider a certain theory of 3-forms in 7 dimensions, and study its dimensional reduction to 4D, compactifying the 7-dimensional manifold on the 3-sphere of a fixed radius. We show that the resulting 4D theory is (Riemannian) General Relativity (GR) in Plebanski formulation, modulo corrections that are negligible for curvatures smaller than Planckian. Possibly the most interesting point of this construction is that the dimensionally reduced theory is GR with a non-zero cosmological constant, and the value of the cosmological constant is directly related to the size of S3. Realistic values of Λ correspond to S3 of Planck size.

Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments.

Consider a lower-dimensional solitonic structure embedded in a higher-dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space, etc. By extending the Landau dynamics approach [Phys. Rev. Lett. 93, 240403 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.240403], we show that it is possible to capture the transverse dynamical modes (the "Kelvin modes") of the undulation of this "soliton filament" within the higher-dimensional space. These are the transverse stability or instability modes and are the ones potentially responsible for the breakup of the soliton into structures such as vortices, vortex rings, etc. We present the theory and case examples in 2D and 3D, corroborating the results by numerical stability and dynamical computations.

Formal higher-spin theories and Kontsevich–Shoikhet–Tsygan formality

The formal algebraic structures that govern higher-spin theories within the unfolded approach turn out to be related to an extension of the Kontsevich formality, namely, the Shoikhet–Tsygan formality. Effectively, this allows one to construct the Hochschild cocycles of higher-spin algebras that make the interaction vertices. As an application of these results we construct a family of Vasiliev-like equations that generate the Hochschild cocycles with sp(2n) symmetry from the corresponding cycles. A particular case of sp(4) may be relevant for the on-shell action of the 4d theory. We also give the exact equations that describe propagation of higher-spin fields on a higher-spin flat background. The consistency of formal higher-spin theories turns out to have a purely geometric interpretation: there exists a certain symplectic invariant associated to cutting a polytope into simplices, namely, the Alexander–Spanier cocycle.

Exact deconstruction of the 6D (2,0) theory

The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T2, starting from a four-dimensional mathcal{N}=2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D mathcal{N}=2 quiver to the “half-BPS” limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S4 to the (2,0) partition function on S4× T2. In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

CT for higher derivative conformal fields and anomalies of (1, 0) superconformal 6d theories

In [8] we proposed the linear relations between the Weyl anomaly c1, c2, c3 coefficients and the 4 coefficients in the chiral anomaly polynomial for (1,0) superconformal 6d theories. These relations were determined up to one free parameter ξ and its value was then conjectured using some additional assumptions. A different value for ξ was recently suggested in arXiv:1702.03518 using an alternative method. Here we confirm that this latter value is indeed the correct one by providing an additional data point: the Weyl anomaly coefficient c3 for the higher derivative (1,0) superconformal 6d vector multiplet. This multiplet contains the 4-derivative conformal gauge vector, 3-derivative fermion and 2-derivative scalar. We find the corresponding value of c3 which is proportional to the coefficient CT in the 2-point function of stress tensor using its relation to the first derivative of the Renyi entropy or the second derivative of the free energy on the product of thermal circle and 5d hyperbolic space. We present some general results of the computation of the Rényi entropy and CT from the partition function on S1 × ℍd − 1 for higher derivative conformal scalars, spinors and vectors in even dimensions. We also give an independent derivation of the conformal anomaly coefficients of the 6d higher derivative vector multiplet from the Seeley-DeWitt coefficients on an Einstein background.

Drag Produced by Waves Trapped at a Density Interface in Nonhydrostatic Flow over an Axisymmetric Hill

Abstract Linear nonhydrostatic theory is used to evaluate the drag produced by 3D trapped lee waves forced by an axisymmetric hill at a density interface. These waves occur at atmospheric temperature inversions, for example, at the top of the boundary layer, and contribute to low-level drag possibly misrepresented as turbulent form drag in large-scale numerical models. Unlike in 2D waves, the drag has contributions from a continuous range of wavenumbers forced by the topography, because the waves can vary their angle of incidence to match the resonance condition. This leads to nonzero drag for Froude numbers (Fr) both <1 and >1 and a drag maximum typically for Fr slightly below 1, with lower magnitude than in hydrostatic conditions owing to wave dispersion. These features are in good agreement with laboratory experiments using two axisymmetric obstacles, particularly for the lower obstacle, if the effects of a rigid lid above the upper layer and friction are taken into account. Quantitative agreement is less satisfactory for the higher obstacle, as flow nonlinearity increases. However, even in that case the model still largely outperforms both 3D hydrostatic and 2D nonhydrostatic theories, emphasizing the importance of both 3D and nonhydrostatic effects. The associated wave signatures are dominated by transverse waves for Fr lower than at the drag maximum, a dispersive “Kelvin ship-wave” pattern near the maximum, and divergent waves for Fr beyond the maximum. The minimum elevation at the density-interface depression existing immediately downstream of the obstacle is significantly correlated with the drag magnitude.

Causality in 3D massive gravity theories

We study the constraints coming from local causality requirement in various $2+1$ dimensional dynamical theories of gravity. In topologically massive gravity, with a single parity non-invariant massive degree of freedom, and in new massive gravity, with two massive spin-$2$ degrees of freedom, causality and unitarity are compatible with each other and both require the Newton's constant to be negative. In their extensions, such as the Born-Infeld gravity and the minimal massive gravity the situation is similar and quite different from their higher dimensional counterparts, such as quadratic (e.g., Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in conflict. We study the problem both in asymptotically flat and asymptotically anti-de Sitter spaces.

Radiation force and torque of light-sheets

The aim of this work is to provide exact analytical closed-form expressions for the longitudinal and transverse optical radiation force and axial spin torque components, for a 2D surface cross-section with arbitrary shape in the field of light-sheet beams of arbitrary wavefront. Generalized partial-wave series expressions for the longitudinal and transverse optical radiation forces and torque are derived based on the multipole expansion in cylindrical wave functions, stemming from series expansions for the incident and scattered electromagnetic fields. The incident light-sheet wavefields are expressed using generalized series involving the beam-shape coefficients (BSCs), and the scattered fields are given in terms of series involving the scattering coefficients of the object. Numerical illustrative examples on a dielectric absorptive circular cylindrical cross-section are provided for different wavefronts, ranging from plane waves, as well as non-paraxial scalar Airy and Gaussian light-sheet beams. The BSCs are derived based on the angular spectrum decomposition method, which provides adequate means to evaluate the radiation force and torque components when the cylinder cross-section is centered on the beam, or shifted off-axially with respect to the incident axis of wave propagation. In essence, the present theoretical analysis provides a complete formalism in the framework of the generalized Lorenz–Mie theory in 2D based upon exact closed-form series expressions to compute the optical force and torque components induced by 2D light-sheets of arbitrary wavefronts, illuminating a scatterer with an arbitrary geometrical cross-section (in 2D). Possible applications are in particle transport and rotation.

Interpolations from supersymmetric to nonsupersymmetric strings and their properties

The interpolation from supersymmetric to non-supersymmetric heterotic theories is studied, via the Scherk-Schwarz compactification of supersymmetric 6D theories to 4D. A general modular-invariant Scherk-Schwarz deformation is deduced from the properties of the 6D theories at the endpoints, which significantly extends previously known examples. This wider class of non-supersymmetric 4D theories opens up new possibilities for model building. The full one-loop cosmological constant of such theories is studied as a function of compactification radius for a number of cases, and the following interpolating configurations are found: two supersymmetric 6D theories related by a T-duality transformation, with intermediate 4D maximum or minimum at the string scale; a non-supersymmetric 6D theory interpolating to a supersymmetric 6D theory, with the 4D theory possibly having an AdS minimum; a "metastable" non-supersymmetric 6D theory interpolating via a 4D theory to a supersymmetric 6D theory.

Four-dimensional mathcal{N} = 2 supersymmetric theory with boundary as a two-dimensional complex Toda theory

We perform a series of dimensional reductions of the 6d, mathcal{N} = (2, 0) SCFT on S2 × Σ × I × S1 down to 2d on Σ. The reductions are performed in three steps: (i) a reduction on S1 (accompanied by a topological twist along Σ) leading to a supersymmetric Yang-Mills theory on S2 × Σ × I, (ii) a further reduction on S2 resulting in a complex Chern-Simons theory defined on Σ × I, with the real part of the complex Chern-Simons level being zero, and the imaginary part being proportional to the ratio of the radii of S2 and S1, and (iii) a final reduction to the boundary modes of complex Chern-Simons theory with the Nahm pole boundary condition at both ends of the interval I, which gives rise to a complex Toda CFT on the Riemann surface Σ. As the reduction of the 6d theory on Σ would give rise to an mathcal{N} = 2 supersymmetric theory on S2 × I × S1, our results imply a 4d-2d duality between four-dimensional mathcal{N} = 2 supersymmetric theory with boundary and two-dimensional complex Toda theory.

Implications of Lorentz symmetry violation on a 5D supersymmetric model

Field models with [Formula: see text] extra spatial dimensions have a larger [Formula: see text] Lorentz symmetry which is broken down to the standard [Formula: see text] four-dimensional one by the compactification process. By considering Lorentz violating operators in a 5D supersymmetric Wess–Zumino model, which otherwise conserve the standard four-dimensional Poincaré invariance, we show that supersymmetry (SUSY) can be restored upon a simple deformation of the supersymmetric transformations. However, SUSY is not preserved in the effective 4D theory that arises after compactification when the 5D Lorentz violating operators do not preserve [Formula: see text] bulk parity. Our mechanism unveils a possible connection among Lorentz violation and the Scherk–Schwarz mechanism. We also show that parity preserving models, on the other hand, do provide well defined supersymmetric KK models.

Chiral 2d theories from N = 4 SYM with varying coupling

We study 2d chiral theories arising from 4d N = 4 Super-Yang Mills (SYM) with varying coupling τ . The 2d theory is obtained by dimensional reduction of N = 4 SYM on a complex curve with a partial topological twist that accounts for the non-constant τ. The resulting 2d theories can preserve (0,n) with n = 2,4,6,8 chiral supersymmetry, and have a natural realization in terms of strings from wrapped D3-branes in F-theory. We determine the twisted dimensional reduction, as well as the spectrum and anomaly polynomials of the resulting strings in various dimensions. We complement this by considering the dual M-theory configurations, which can either be realized in terms of M5-branes wrapped on complex surfaces, or M2-branes on curves that result in 1d supersymmetric quantum mechanics.

Analytic bounds and emergence of AdS2 physics from the conformal bootstrap

We study analytically the constraints of the conformal bootstrap on the lowlying spectrum of operators in field theories with global conformal symmetry in one and two spacetime dimensions. We introduce a new class of linear functionals acting on the conformal bootstrap equation. In 1D, we use the new basis to construct extremal functionals leading to the optimal upper bound on the gap above identity in the OPE of two identical primary operators of integer or half-integer scaling dimension. We also prove an upper bound on the twist gap in 2D theories with global conformal symmetry. When the external scaling dimensions are large, our functionals provide a direct point of contact between crossing in a 1D CFT and scattering of massive particles in large AdS2. In particular, CFT crossing can be shown to imply that appropriate OPE coefficients exhibit an exponential suppression characteristic of massive bound states, and that the 2D flat-space S-matrix should be analytic away from the real axis.