Supergravity as generalised geometry II: E d ( d ) × ℝ + and M theory

We reformulate eleven-dimensional supergravity, including fermions, in terms of generalised geometry, for spacetimes that are warped products of Minkowski space with a d -dimensional manifold M with d ≤ 7. The reformulation has an E d ( d ) × ℝ + structure group and it has a local ${{\widetilde{H}}_d}$ symmetry, where ${{\widetilde{H}}_d}$ is the double cover of the maximally compact subgroup of E d ( d ) . The bosonic degrees for freedom unify into a generalised metric, and, defining the generalisked analogue D of the Levi-Civita connection, one finds that the corresponding equations of motion are the vanishing of the generalised Ricci tensor. To leading order, we show that the fermionic equations of motion, action and supersymmetry variations can all be written in terms of D . Although we will not give the detailed decompositions, this reformulation is equally applicable to type IIA or IIB supergravity restricted to a ( d − 1)-dimensional manifold. For completeness we give explicit expressions in terms of ${{\widetilde{H}}_4}$ = Spin(5) and ${{\widetilde{H}}_7}$ = SU(8) representations for d = 4 and d = 7

Finite gauge transformations and geometry in double field theory

Recently proposed forms for gauge transformations with finite parameters in double field theory are discussed and problematic issues are identified. A new form for finite gauge transformations is derived that reveals the underlying gerbe structure and the close relationship with generalised geometry. The nature of generalised tensors is elucidated, and in particular it is seen that the presence of a constant metric with split signature does not restrict the doubled geometry, provided it is a generalised tensor rather than a conventional tensor

Supersymmetry for gauged double field theory and generalised Scherk–Schwarz reductions

Previous constructions of supersymmetry for double field theory have relied on the so-called strong constraint. In this paper, the strong constraint is relaxed and the theory is shown to possess supersymmetry once the generalised Scherk–Schwarz reduction is imposed. The equivalence between the generalised Scherk–Schwarz reduced theory and the gauged double field theory is then examined in detail for the supersymmetric theory. As a biproduct we write the generalised Killing spinor equations for the supersymmetric double field theory

Highest weight generating functions for Hilbert series

We develop a new method for representing Hilbert series based on the highest weight Dynkin labels of their underlying symmetry groups. The method draws on plethystic functions and character generating functions along with Weyl integration. We give explicit examples showing how the use of such highest weight generating functions (“HWGs”) permits an efficient encoding and analysis of the Hilbert series of the vacuum moduli spaces of classical and exceptional SQCD theories and also of the moduli spaces of instantons. We identify how the HWGs of gauge invariant operators of a selection of classical and exceptional SQCD theories result from the interaction under symmetrisation between a product group and the invariant tensors of its gauge group. In order to calculate HWGs, we derive and tabulate character generating functions for low rank groups by a variety of methods, including a general character generating function, based on the Weyl Character Formula, for any classical or exceptional group

Coulomb branch and the moduli space of instantons

The moduli space of instantons on ℂ 2 for any simple gauge group is studied using the Coulomb branch of N = 4 $$\mathcal{N}=4$$ gauge theories in three dimensions. For a given simple group G , the Hilbert series of such an instanton moduli space is computed from the Coulomb branch of the quiver given by the over-extended Dynkin diagram of G . The computation includes the cases of non-simply-laced gauge groups G , complementing the ADHM constructions which are not available for exceptional gauge groups. Even though the Lagrangian description for non-simply laced Dynkin diagrams is not currently known, the prescription for computing the Coulomb branch Hilbert series of such diagrams is very simple. For instanton numbers one and two, the results are in agreement with previous works. New results and general features for the moduli spaces of three and higher instanton numbers are reported and discussed in detail

The Renormalization Group flow of unimodular f(R) gravity

Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quantum theory based on the asymptotic safety scenario is studied, and evidence for an interacting fixed point in unimodular f ( R ) gravity is found. We study the fixed point and its properties, and also discuss the compatibility of unimodular asymptotic safety with dynamical matter, finding evidence for its compatibility with the matter degrees of freedom of the Standard Model

Emergent time and the M5-brane

We consider the maximal super-Yang-Mills theory in 5 Euclidean dimensions with SO(5) R-symmetry and 16 supersymmetries. We argue that the strong coupling limit of this theory (with a possible UV completion) has an emergent time dimension and gives a description of the 5+1 dimensional Lorentz invariant (2, 0) theory of the M5-brane, compactified on a timelike circle with radius R = g 2 /4 π 2 . Our discussion involves issues of quantization of Euclidean theories without time

Braneworld localisation in hyperbolic spacetime

We present a construction employing a type IIA supergravity and 3-form flux background together with an NS5-brane that localises massless gravity near the 5-brane worldvolume. The nonsingular underlying type IIA solution is a lift to 10D of the vacuum solution of the 6D Salam-Sezgin model and has a hyperbolic H 2 2 × S 1 $${\mathrm{\mathcal{H}}}^{\left(2,2\right)}\times {S}^1$$ structure in the lifting dimensions. A fully back-reacted solution including the NS5-brane is constructed by recognising the 10D Salam-Sezgin vacuum solution as a “brane resolved through transgression.” The background hyperbolic structure plays a key rôle in generating a mass gap in the spectrum of the transverse-space wave operator, which gives rise to the localisation of gravity on the 6D NS5-brane worldvolume, or, equally, in a further compactification to 4D. Also key to the successful localisation of gravity is the specific form of the corresponding transverse wavefunction Schrödinger problem, which asymptotically involves a V = −1 / (4 ρ 2 ) potential, where ρ is the transverse-space radius, and for which the NS5-brane source gives rise to a specific choice of self-adjoint extension for the transverse wave operator. The corresponding boundary condition as ρ → 0 ensures the masslessness of gravity in the effective braneworld theory. Above the mass gap, there is a continuum of massive states which give rise to small corrections to Newton’s law

Characterising dark matter searches at colliders and direct detection experiments: vector mediators

We introduce a Minimal Simplified Dark Matter (MSDM) framework to quantitatively characterise dark matter (DM) searches at the LHC. We study two MSDM models where the DM is a Dirac fermion which interacts with a vector and axial-vector mediator. The models are characterised by four parameters: m DM , M med , g DM and g q , the DM and mediator masses, and the mediator couplings to DM and quarks respectively. The MSDM models accurately capture the full event kinematics, and the dependence on all masses and couplings can be systematically studied. The interpretation of mono-jet searches in this framework can be used to establish an equal-footing comparison with direct detection experiments. For theories with a vector mediator, LHC mono-jet searches possess better sensitivity than direct detection searches for light DM masses (≲5 GeV). For axial-vector mediators, LHC and direct detection searches generally probe orthogonal directions in the parameter space. We explore the projected limits of these searches from the ultimate reach of the LHC and multi-ton xenon direct detection experiments, and find that the complementarity of the searches remains. Finally, we provide a comparison of limits in the MSDM and effective field theory (EFT) frameworks to highlight the deficiencies of the EFT framework, particularly when exploring the complementarity of mono-jet and direct detection searches

The thermoelectric properties of inhomogeneous holographic lattices

We consider inhomogeneous, periodic, holographic lattices of D = 4 Einstein-Maxwell theory. We show that the DC thermoelectric conductivity matrix can be expressed analytically in terms of the horizon data of the corresponding black hole solution. We numerically construct such black hole solutions for lattices consisting of one, two and ten wave-numbers. We numerically determine the AC electric conductivity which reveals Drude physics as well as resonances associated with sound modes. No evidence for an intermediate frequency scaling regime is found. All of the monochromatic lattice black holes that we have constructed exhibit scaling behaviour at low temperatures which is consistent with the appearance of Ad S 2 × ℝ 2 $$Ad{S}_2\times {\mathrm{\mathbb{R}}}^2$$ in the far IR at T = 0