Past String Theory Seminar

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.

The 3d/3d correspondence is about the correspondence between 3d N=2 supersymmetric gauge theories and the 3d complex Chern-Simons theory on a 3-manifold.

In this talk I will describe codimension 2 and 4 supersymmetric defects in this correspondence, by a combination of various existing techniques, such as state-integral models, cluster algebras, holographic dual, and 5d SYM.

In this talk, gauged quiver quantum mechanics will be analysed for BPS state counting. Despite the wall-crossing phenomenon of those countings, an invariant quantity of quiver itself, dubbed quiver invariant, will be carefully defined for a certain class of abelian quiver theories. After that, to get a handle on nonabelian theories, I will overview the abelianisation and the mutation methods, and will illustrate some of their interesting features through a couple of simple examples.

It has been conjectured that the fundamental theory of strings and branes has an $E_{11}$ symmetry. I will explain how this conjecture  leads to  a generalised space-time,  which is automatically equipped with its own geometry, as well as equations of motion for the fields that live on this generalised space-time.

 

Form factors form a bridge between the purely on-shell amplitudes and the purely off-shell correlation functions. In this talk, we study the form factors of general gauge-invariant local composite operators in N=4 SYM theory via on-shell methods. At tree-level and for a minimalnumber of external fields, the form factor exactly realises the spin-chain picture of N=4 SYM theory in the language of scattering amplitudes. Via generalised unitarity, we obtain the cut-constructible part of the one-loop correction to the minimal form factor of a generic operator. Its UV divergence yields the complete one-loop dilatation operator of the theory. At two-loop order, we employ unitarity to calculate the minimal form factors and thereby the dilatation operator for the Konishi primary operator and all operators in the SU(2) sector. For the former operator as well as other non-protected operators, important subtleties arise which require an extension of the method of unitarity.

Recently, as part of a project to find CY manifolds for which both the Hodge numbers (h^{11}, h^{21}) are small, manifolds have been found with Hodge numbers (4,1) and (1,1). The one-dimensional special geometries of their complex structures are more complicated than those previously studied. I will review these, emphasising the role of the fundamental period and Picard-Fuchs equation. Two arithmetic aspects arise: the first is the role of \zeta(3) in the monodromy matrices and the second is the fact, perhaps natural to a number theorist, that through a study of the CY manifolds over finite fields, modular functions can be associated to the singular manifolds of the family. This is a report on joint work with Volker Braun, Xenia de la Ossa and Duco van Straten.

We propose a non-perturbative formulation of structure constants of single trace operators in planar N=4 SYM.  We match our results with both weak and strong coupling data available in the literature. Based on work with Benjamin Basso and Pedro Vieira.

I shall demonstrate, under some mild assumptions, that the symmetry group of  extreme, Killing, supergravity horzions contains an sl(2, R) subalgebra.  The proof requires a generalization of the  Lichnerowicz theorem for non-metric connections. The techniques developed can also be applied in the classification
of AdS and Minkowski flux backgrounds.
 

I will discuss how singular fibers in higher codimension in elliptically fibered Calabi-Yau fourfolds can be studied using Coulomb branch phases for d=3 supersymmetric gauge theories. This approach gives an elegent description of the generalized Kodaira fibers in terms of combinatorial/representation-theoretic objects called "box graphs", including the network of flops connecting distinct small resolutions. For physics applications, this approach can be used to constrain the possible matter spectra and possible U(1) charges (models with higher rank Mordell Weil group) for F-theory GUTs.

I will speak about weak Fano 3-folds, K3 surfaces and their Picard lattices, and explain how to solve the matching problem in various situations

Motivated by the study of supersymmetric backgrounds with non-trivial fluxes, we provide a formulation of supergravity in the language of generalised geometry, as first introduced by Hitchin, and its extensions. This description both dramatically simplifies the equations of the theory by making the hidden symmetries manifest, and writes the bosonic sector geometrically as a direct analogue of Einstein gravity. Further, a natural analogue of special holonomy manifolds emerges and coincides with the conditions for supersymmetric backgrounds with flux, thus formulating these systems as integrable geometric structures.
 

The chiral scalar superfield has interesting BRST cohomology, but the relevant cohomology objects all  have spinor indices. So they cannot occur in an action. They need to be coupled to a chiral dotted spinor superfield. Until now, this has been very problematic, since no sensible action for a chiral dotted spinor superfield was known.  The most obvious such action contains higher derivatives and tachyons.

Now,  a sensible  action has been found. When coupled to the cohomology, this action removes the supersymmetry charge from the theory while maintaining the rigidity and power of supersymmetry.The simplest example of this phenomenon has exactly the fermion content of the Leptons or the Quarks.  The mechanism has the potential to get around the cosmological constant problem, and also the problem of the sum rules of spontaneously broken supersymmetry.