Forthcoming events in this series
Global Aspects of F-theory on singular CY fourfolds
Abstract
String compactifications on SU(3) structure manifolds
Abstract
In the absence of background fluxes and sources, the compactification of string theories on Calabi-Yau threefolds leads to supersymmetric solutions.Turning on fluxes, e.g. to lift the moduli of the compactification, generically forces the geometry to break the Calabi-Yau conditions, and to satisfy, instead, the weaker condition of reduced structure. In this talk I will discuss manifolds with SU(3) structure, and their relevance for heterotic string compacitications. I will focus on domain wall solutions and how explicit example geometries can be constructed.
A Metric for Heterotic Moduli
Abstract
The Hodge Plot of Toric Calabi-Yau Threefolds. Webs of K3 Fibrations from Polyhedra with Interchangeable Parts
Abstract
Lines on the Dwork Pencil of Quintic Threefolds
Abstract
Instanton - a window into physics of M5-branes
Abstract
Instantons and W-bosons in 5d N=2 Yang-Mills theory arise from a circle
compactification of the 6d (2,0) theory as Kaluza-Klein modes and winding
self-dual strings, respectively. We study an index which counts BPS
instantons with electric charges in Coulomb and symmetric phases. We first
prove the existence of unique threshold bound state of U(1) instantons for
any instanton number. By studying SU(N) self-dual strings in the Coulomb
phase, we find novel momentum-carrying degrees on the worldsheet. The total
number of these degrees equals the anomaly coefficient of SU(N) (2,0) theory.
We finally propose that our index can be used to study the symmetric phase of
this theory, and provide an interpretation as the superconformal index of the
sigma model on instanton moduli space.
Double Field Theory and the Geometry of Duality
Abstract
String theory on a torus requires the introduction of dual coordinates
conjugate to string winding number. This leads to physics and novel geometry in a doubled space. This will be
compared to generalized geometry, which doubles the tangent space but not the manifold.
For a d-torus, string theory can be formulated in terms of an infinite
tower of fields depending on both the d torus coordinates and the d dual
coordinates. This talk focuses on a finite subsector consisting of a metric
and B-field (both d x d matrices) and a dilaton all depending on the 2d
doubled torus coordinates.
The double field theory is constructed and found to have a novel symmetry
that reduces to diffeomorphisms and anti-symmetric tensor gauge
transformations in certain circumstances. It also has manifest T-duality
symmetry which provides a generalisation of the usual Buscher rules to
backgrounds without isometries. The theory has a real dependence on the full
doubled geometry: the dual dimensions are not auxiliary. It is concluded
that the doubled geometry is physical and dynamical.
N=2 Gauge Theories: Congruence Subgroups, Coset Graphs and Modular Surfaces
Abstract
We establish a correspondence between generalized quiver gauge theories in
four dimensions and congruence subgroups of the modular group, hinging upon
the trivalent graphs which arise in both. The gauge theories and the graphs
are enumerated and their numbers are compared. The correspondence is
particularly striking for genus zero torsion-free congruence subgroups as
exemplified by those which arise in Moonshine. We analyze in detail the
case of index 24, where modular elliptic K3 surfaces emerge: here, the
elliptic j-invariants can be recast as dessins d'enfant which dictate the
Seiberg-Witten curves.
Integer Partitions, Mirror Symmetry and 3d Gauge Theories
Abstract
In this talk, I will focus on an infinite class of 3d N=4 gauge theories
which can be constructed from a certain set of ordered pairs of integer
partitions. These theories can be elegantly realised on brane intervals in
string theory. I will give an elementary review on such brane constructions
and introduce to the audience a symmetry, known as mirror symmetry, which
exchanges two different phases (namely the Higgs and Coulomb phases) of such
theories. Using mirror symmetry as a tool, I will discuss a certain
geometrical aspect of the vacuum moduli spaces of such theories in the
Coulomb phase. It turns out that there are certain infinite subclasses of
such spaces which are special and rather simple to study; they are complete intersections. I will mention some details and many interesting features of these spaces.
A simple formula for gravitational MHV amplitudes
Abstract
A simple formula is given for the $n$-field tree-level MHV gravitational
amplitude, based on soft limit factors. It expresses the full $S_n$ symmetry
naturally, as a determinant of elements of a symmetric ($n \times n$) matrix.
Gauge-Strings Duality and applications
Abstract
I will discuss some recent progress connecting different quiver gauge theories and some applications of these results.
Three-sphere partition function, counterterms and supergravity
Abstract
The partition function of 3d N=2 superconformal theories on the
3-sphere can be computed exactly by localization methods. I will explain
some sublteties associated to that important result. As a by-product, this
analysis establishes the so-called F-maximization principle for N=2 SCFTs in
3d: the exact superconformal R-charge maximizes the 3-sphere free energy
F=-log Z.
Holographic stripes and helical superconductors
Abstract
The AdS/CFT correspondence is a powerful tool to analyse strongly coupled quantum field
theories. Over the past few years there has been a surge of activity aimed at finding
possible applications to condensed matter systems. One focus has been to holographically
realise various kinds of phases via the construction of fascinating new classes of black
hole solutions. In this framework, I will discuss the possibility of describing finite
temperature phase transitions leading to spontaneous breaking of translational invariance of
the dual field theory at strong coupling. Along with the general setup I will also discuss
specific string/M theory embeddings of the corresponding symmetry breaking modes leading to
the description of such phases.
M-theory dualities and generalised geometry
Abstract
In this talk we will review M-theory dualities and recent attempts to make these dualities manifest in eleven-dimensional supergravity. We will review the work of Berman and Perry and then outline a prescription, called non-linear realisation, for making larger duality symmetries manifest. Finally, we will explain how the local symmetries are described by generalised geometry, which leads to a duality-covariant constraint that allows one to reduce from generalised space to physical space.
Quantum states to brane geometries via fuzzy moduli space
Abstract
The moduli space of supersymmetric (eighth-BPS) giant gravitons in $AdS_5 \times S^5$ is a limit of projective spaces. Quantizing this moduli space produces a Fock space of oscillator states, with a cutoff $N$ related to the rank of the dual $U(N)$ gauge group. Fuzzy geometry provides the ideal set of techniques for associating points or regions of moduli space to specific oscillator states. It leads to predictions for the spectrum of BPS excitations of specific worldvolume geometries. It also leads to a group theoretic basis for these states, containing Young diagram labels for $U(N)$ as well as the global $U(3)$ symmetry group. The problem of constructing gauge theory operators corresponding to the oscillator states and some recent progress in this direction are explained.
The MSSM spectrum from the heterotic standard embedding
Abstract
I will describe the recent construction of new supersymmetric compactifications of the heterotic string which yield just the spectrum of the MSSM at low energies. The starting point is the standard embedding solution on a Calabi-Yau manifold with Euler number -6 with various choices of Wilson lines, i.e., various choices of discrete holonomy for the gauge bundle. Although they yield three net generations of standard model matter, such models necessarily have a larger gauge group than the standard model, as well as exotic matter content. Families of stable bundles can be obtained by deformation of these simple solutions, the deformation playing the dual role of partially breaking the gauge group and reducing the matter content, and in this way we construct more realistic models. The moduli space breaks up into various branches depending on the initial choice of Wilson lines, and on eight of these branches we find models with exactly the standard model gauge group, three generations of quarks and leptons, two Higgs doublets, and no other massless charged states. I will also comment on why these are possibly the unique models of this type.
Singularity structure and massless dyons of pure N = 2, d = 4 theories with SU(r+1) and Sp(2r) gauge groups
Abstract
We study pure Seiberg-Witten theories with $SU(r+1)$ and $Sp(2r)$ gauge groups with no flavors. We study singularity loci of moduli space of the Seiberg-Witten curve. Using exterior derivative and discriminant operators, we can find Argyres-Douglas loci of the SW theory. We also compute BPS charges of the massless dyons of $SU$ and $Sp$ SW theory. In a detailed example of $C_2=Sp(4)$, we find 6 points in the moduli space where we have 2 massless BPS dyons, and 3 of them give Argyres-Douglas loci. We show that BPS charges of the massless dyons jump as we go across Argyres-Douglas loci, giving an explicit example of Argyres-Douglas loci living inside the wall of marginal stability. (Based on work in progress with Keshav Dasgupta)
Giant Gravitons in the ABJM Duality
Abstract
I shall describe the construction of the four-brane giant graviton on $\mathrm{AdS}_4\times \mathbb{CP}^3$ (extended and moving in the complex projective space), which is dual to a subdeterminant operator in the ABJM model. This dynamically stable, BPS configuration factorizes at maximum size into two topologically stable four-branes (each wrapped on a different $\mathbb{CP}^2 \subset \mathbb{CP}^3$ cycle) dual to ABJM dibaryons. Our study of the spectrum of small fluctuations around this four-brane giant provides good evidence for a dependence in the spectrum on the size, $\alpha_0$, which is a direct result of the changing shape of the giant’s worldvolume as it grows in size. I shall finally comment upon the implications for operators in the non-BPS, holomorphic sector of the ABJM model.
Generalized quark-antiquark potential of N=4 SYM at weak and strong coupling
Abstract
I will present a two-parameter family of Wilson loop operators in N = 4 supersymmetric Yang-Mills theory which interpolates smoothly between the 1/2 BPS line or circle and a pair of antiparallel lines. These observables capture a natural generalization of the quark-antiquark potential. These loops are calculated on the gauge theory side to second order in perturbation theory and in a semiclassical expansion in string theory to one-loop order. The resulting determinants are given in integral form and can be evaluated numerically for general values of the parameters or analytically in a systematic expansion around the 1/2 BPS configuration. I will comment about the feasibility of deriving all-loop results for these Wilson loops.
Emergent IR CFTs in black hole physics
Abstract
I will discuss the dynamical emergence of IR conformal invariance describing the low energy excitations of near-extremal R-charged global AdS${}_5$ black holes. To keep some non-trivial dynamics in the sector of ${\cal N}=4$ SYM captured by the near horizon limits describing these IR physics, we are lead to study large N limits in the UV theory involving near vanishing horizon black holes. I will consider both near-BPS and non-BPS regimes, emphasising the differences in the local AdS${}_3$ throats emerging in both cases. I will compare these results with the predictions obtained by Kerr/CFT, obtaining a natural quantisation for the central charge of the near-BPS emergent IR CFT describing the open strings stretched between giant gravitons.
Gravity duals of supersymmetric gauge theories on curved manifolds
Abstract
In just the last year it has been realized that one can define supersymmetric gauge theories on non-trivial compact curved manifolds, coupled to a background R-symmetry gauge field, and moreover that expectation values of certain BPS operators reduce to finite matrix integrals via a form of localization. I will argue that a general approach to this topic is provided by the gauge/gravity correspondence. In particular, I will present several examples of supersymmetric gauge theories on different 1-parameter deformations of the three-sphere, which have a large N limit, together with their gravity duals (which are solutions to Einstein-Maxwell theory). The Euclidean gravitational partition function precisely matches a large N matrix model evaluation of the field theory partition function, as an exact \emph{function} of the deformation parameter.
Scattering and Sequestering of Blow-Up Moduli in Local String Models
Abstract
I will study the sequestering of blow-up fields through a CFT in a toroidal orbifold setting. In particular, I will examine the disk correlator between orbifold blow-up moduli and matter Yukawa couplings. Blow-up moduli appear as twist fields on the worldsheet which introduce a monodromy
condition for the coordinate field X. Thus I will focus on how the presence of twist field affects
the CFT calculation of disk correlators. Further, I will explain how the results are relevant to
suppressing soft terms to scales parametrically below the gravitino mass. Last, I want to explore the
relevance of our calculation for the case of smooth Calabi-Yaus.
Landscape of consistent reductions with applications
Abstract
Consistent truncations have proved to be powerful tools in the construction of new string theory solutions. Recently, they have been employed in the holographic description of condensed matter systems. In the talk, I will present a rich class of supersymmetric consistent truncations of higher-dimensional supergravity which are based on geometric structures, focusing on the tri-Sasakian case. Then I will discuss some applications, including a general result relating AdS backgrounds to solutions with non-relativistic Lifshitz symmetry.