A large number of examples of compact G2 manifolds, relevant to supersymmetric compactifications of M-Theory to four dimensions, can be constructed by forming a twisted connected sum of two appropriate building blocks times a circle. These building blocks, which are appropriate K3-fibred threefolds, are shown to have a natural and elegant construction in terms of tops, which parallels the construction of Calabi-Yau manifolds via reflexive polytopes.

# Past String Theory Seminar

I will consider higher derivative corrections to the graviton 3-point coupling within a weakly coupled theory of gravity. Lorentz invariance allows further structures beyond that of Einstein’s theory. I will argue that these structures are constrained by causality, and show that the problem cannot be fixed by adding conventional particles with spins J ≤ 2, but adding an infinite tower of massive particles with higher spins. Implications of this result in the context of AdS/CFT, quantum gravity in asymptotically flat space-times, and non-Gaussianity features of primordial gravitational waves are discussed.

It is unknown whether a bound on axion field ranges exists within quantum gravity. We study axion field ranges using extended supersymmetry, in particular allowing an analysis within strongly coupled regions of moduli space. We apply this strategy to Calabi-Yau compactifications with one and two Kähler moduli. We relate the maximally allowable decay constant to geometric properties of the underlying Calabi-Yau geometry. In all examples we find a maximal field range close to the reduced Planck mass (with the largest field range being 3.25 $M_P$). On this perspective, field ranges relate to the intersection and instanton numbers of the underlying Calabi-Yau geometry.

I will give an introductory account of the zeta-functions for one-parameter families of CY manifolds. The aim of the talk is to point out that the zeta-functions corresponding to singular manifolds of the family correspond to modular forms. In order to give this introductory account I will give a lightning review of finite fields and of the p-adic numbers.

It has been recently pointed out that maximal gauged supergravities in four dimensions often come in one-parameter families. The parameter measures the combination of electric and magnetic vectors that participate in the gauging. I will discuss the higher-dimensional origin of these dyonic gaugings, when the gauge group is chosen to be ISO(7). This gauged supergravity arises from consistent truncation of massive type IIA on the six-sphere, with its dyonically-gauging parameter identified with the Romans mass. The (AdS) vacua of the 4D supergravity give rise to new explicit AdS4 backgrounds of massive type IIA. I will also show that the 3D field theories dual to these AdS4 solutions are Chern-Simons-matter theories with a simple gauge group and level k also given by the Romans mass.

Two interesting properties of static curved space QFTs are Casimir Energies, and the Energy Gaps of fluctuations. We investigate what AdS/CFT has to say about these properties by examining holographic CFTs defined on curved but static spatially closed spacetimes. Being holographic, these CFTs have a dual gravitational description under Gauge/Gravity duality, and these properties of the CFT are reflected in the geometry of the dual bulk. We can turn this on its head and ask, what does the existence of the gravitational bulk dual imply about these properties of the CFTs? In this talk we will consider holographic CFTs where the dual vacuum state is described by pure Einstein gravity with negative cosmological constant. We will argue using the bulk geometry first, that if the CFT spacetime's spatial scalar curvature is positive there is a lower bound on the gap for scalar fluctuations, controlled by the minimum value of the boundary Ricci scalar. In fact, we will show that it is precisely the same bound as is satisfied by free scalar CFTs, suggesting that this bound might be something that applies more generally than just in a Holographic context. We will then show, in the case of 2+1 dimensional CFTs, that the Casimir energy is non-positive, and is in fact negative unless the CFT's scalar curvature is constant. In this case, there is no restriction on the boundary scalar curvature, and we can even allow singularities in the bulk, so long as they are 'good' singularities. If time permits, we will also describe some new results about the Hawking-Page transition in this context.

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincare. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,NL =1)and(3+0,NR =0).

We review some recent progress in computing massless spectra and moduli in heterotic string compactifications. In particular, it was recently shown that the heterotic Bianchi Identity can be accounted for by the construction of a holomorphic operator. Mathematically, this corresponds to a holomorphic double extension. Moduli can then be computed in terms of cohomologies of this operator. We will see how the same structure can be derived form a Gukov-Vafa-Witten type superpotential. We note a relation between the lifted complex structure and bundle moduli, and cover some examples, and briefly consider obstructions and Yukawa couplings arising from these structures.

Calabi-Yau manifolds without flux are perhaps the best-known

supergravity backgrounds that leave some supersymmetry unbroken. The

supersymmetry conditions on such spaces can be rephrased as the

existence and integrability of a particular geometric structure. When

fluxes are allowed, the conditions are more complicated and the

analogue of the geometric structure is not well understood.

In this talk, I will define the analogue of Calabi-Yau geometry for

generic D=4, N=2 backgrounds with flux in both type II and

eleven-dimensional supergravity. The geometry is characterised by a

pair of G-structures in 'exceptional generalised geometry' that

interpolate between complex, symplectic and hyper-Kahler geometry.

Supersymmetry is then equivalent to integrability of the structures,

which appears as moment maps for diffeomorphisms and gauge

transformations. Similar structures also appear in D=5 and D=6

backgrounds with eight supercharges.

As a simple application, I will discuss the case of AdS5 backgrounds

in type IIB, where deformations of these geometric structures give

exactly marginal deformations of the dual field theories.