Australia and New Zealand Geometry, Strings and Fields Seminar Series
The meetings are roughly monthly. Friendly discussion, questions and comments are encouraged. Our dream is to create a space where we can foster new collaboration and projects between researchers in Australian, New Zealand and beyond.
The seminar series was initiated by Jock McOrist (University of New England), Johanna Knapp (University of Melbourne) and Gabriele Tartaglino-Mazzucchelli (University of Queensland). If you are interested in joining the mailing list email Jock McOrist (UNE) with a request.
We have a youtube channel which you can subscribe to here.
Date: Friday 1 December 2023.
Title: S-duality in field theory
Abstract: After defining S duality, I focus on the oldest and best-studied examples: S-duality in 4-dimensional maximally supersymmetric Yang-Mills theories. I review the gradual refinement of the predictions of S-duality over the past 4 decades or so, and end with some recent results and open questions.
Date: Friday 15 September 2023.
Title: Symplectic cuts and open/closed strings
Abstract: In this talk, we introduce a concrete relation between genus zero closed Gromov-Witten invariants of Calabi-Yau threefolds and genus zero open Gromov-Witten invariants of a Lagrangian A-brane in the same threefold. Via a quantum uplift of the symplectic cut construction, which we describe in terms of an equivariant gauged linear sigma model, we define the notion of a quantum Lebesgue measure associated to the A-brane. On the one hand, integration of this measure w.r.t. the open string modulus recovers the equivariant quantum volume of the whole CY3, thereby encoding closed GW invariants. On the other hand, the monodromy of the quantum measure around cycles in Kähler moduli space encodes open GW invariants of the Lagrangian A-brane. Based on 2306.07329 and upcoming work with Pietro Longhi and Maxim Zabzine.
Date: Friday 23 June 2023
Title: Parallel surface defects in gauge theory and quantization of Hitchin system
Abstract: I'll explain how the quantization of Hitchin integrable system can be formulated in the N=2 supersymmetric gauge theory with the help of half-BPS surface defects. We consider two types of surface defects, the "canonical" surface defect and the "regular monodromy" surface defect, inserted on top of each other. The correlation function of the surface defects is shown to give a basis of coinvariants with the twisted vacuum module. The insertion of twisted vacuum module is known to give the action of Hecke modification on the coinvariants. I'll define the Hecke operator as an integral of the image of Hecke modifications, which is shown to factorize due to the cluster decomposition of the two surface defects. The factorization explains why the action of the Hecke operator is diagonal. Using this factorization property and the relation with the universal oper, I show the sections of the vev of the regular monodromy surface defect gives common eigenfunctions of the quantum Hitchin Hamiltonians (with the eigenvalues parametrizing the space of opers), explaining the statement of Beilinson and Drinfeld in the N=2 gauge theory framework.
Date: Friday 28 April 2023
Title: Non-Kahler Transitions of Calabi-Yau Threefolds
Abstract: We will describe a process which connects Calabi-Yau threefolds with different topologies by degenerating 2-cycles and introducing new 3-cycles. This operation may produce a non-Kahler complex manifold. In this talk, we will discuss the geometrization of these spaces by special non-Kahler metrics. This is joint work with T.C. Collins and S.-T. Yau.
Date: Tuesday 22 November, 6.30pm AEDT
Title: Aspects of maximally symmetric non-linear (ModMax) electrodynamics
Abstract: We will review properties and peculiarities of a recently found unique non-linear generalization of Maxwell's electrodynamics (dubbed ModMax) that preserves all the symmetries of the former, i.e. conformal invariance and electric-magnetic duality. In particular, we will see that ModMax admits, as exact solutions, plane waves and Lienard-Wiechert fields induced by a moving electric or magnetic particle, or a dyon. Effects of ModMax may manifest themselves in physical phenomena such as vacuum birefringence and in properties of gravitational objects (e.g. charged black holes). ModMax and its Born-Infeld-like generalization arise as TTbar-like deformations of Maxwell's theory and there exist supersymmetric and higher-spin extensions of these models.
Date: Friday 4 November, 2022
Title: Tensionless Strings and the Swampland
Abstract: The aim of this talk is to report on progress towards understanding how string theory realizes general conjectures on the nature of quantum gravity, focusing mostly on four-dimensional theories with minimal supersymmetry. Specifically, we will address two famous conjectures: the Distance Conjecture and the Weak Gravity Conjecture. The former claims that an infinite tower of states should become light near the infinite-distance boundary of the moduli space. According to the recent proposal of the Emergent String Conjecture, this tower should correspond either to a Kaluza-Klein tower or to the excitation tower of a weakly coupled critical string. We will first verify this Emergent String proposal in the framework of geometric F-theory compactifications, by classifying and analyzing infinite distance limits in the Kahler moduli space. We will then argue that the string tower at weak coupling provides a sublattice of particles fulfilling the Weak Gravity Conjecture.
Date: Friday 9 September 2022
Title: Magnetic quivers, Higgs branches, and 6d N=(1,0) theories
Abstract: The physics of M5 branes on an A or D-type ALE singularity exhibits a variety of phenomena that introduce additional massless degrees of freedom. There are tensionless strings whenever two M5 branes coincide. These systems do not admit a low-energy Lagrangian description so new techniques are desirable to shed light on the physics of these phenomena. The 6-dimensional N=(1,0) world-volume theory on the M5 branes is composed of massless vector, tensor, and hyper multiplets, and has two branches of the vacuum moduli space where either the scalar fields in the tensor or hyper multiplets receive vacuum expectation values. Focusing on the Higgs branch of the low-energy theory, a new Higgs branch arises whenever a BPS-string becomes tensionless. Consequently, a single theory admits a multitude of Higgs branches depending on the types of tensionless strings in the spectrum. In this talk, I will review the "magnetic quiver" formalism for M5 branes on A or D-type singularities, introduced in arXiv:1904.12293 and 1912.02773. This technique allows to describe the 6d N=(1,0) Higgs branches over any point of the tensor branch in a concise and effective manner by means of 3d N=4 Coulomb branches of the magnetic quivers. Thereafter, I will extend the setup by allowing for non-trivial boundary conditions on the ALE spaces. Using negatively charged branes in the dual Type IIA brane configurations, I will demonstrate that exciting Higgs branch geometries can be uncovered by using magnetic quivers. For example, a nilpotent orbit closure of E6 and F4. This is part is based on arXiv:2208.07279.
Date: Friday 29 July 2022
Title: q-Opers — what they are and what are they good for?
Abstract: I will introduce the new geometric object - (G,q)-opers on a Riemann surface where G is a simple simply connected Lie algebra. I will describe their applications in geometric Langlands and integrable systems. Using the formalism of (G,q)-opers we can describe a spectrum of quantum integrable models, like XXZ spin chains and their generalizations in representation theory (so called quantum/classical duality). As a different application we can study wall crossing transformations between fundamental solutions of Fuchsian ODEs with regular singularities (ODE/IM correspondence) using (G,q)-oper connections.
Date: Friday 27 May, 2022,
Title: Anti-brane uplifts and goldstino condensates
Abstract: We investigate the formation of composite states of the goldstino in theories with non-linearly realized supersymmetry and show that the pure Volkov-Akulov model has an instability towards goldstino condensation. We discuss the limitations and implications of our findings for string models involving anti-brane uplifts.
Date: Friday 29 April, 2022, 4pm, AEST
Title: Conformal interactions of higher-spin supermultiplets
Abstract: Consistent interactions of gauge fields with spin s > 2, or ‘higher-spin’ fields, are notoriously tricky to formulate. For example, after more than 80 years of scrutiny, a Lagrangian formulation of interacting massless higher-spin fields remains absent. Even less is known about the corresponding supersymmetric theories. In this talk I will provide an overview of a more tractable class of models known as superconformal higher-spin (SCHS) theories. I will also report on new progress towards the formulation of consistent interactions of SCHS gauge supermultiplets with (i) conformal supergravity; (ii) various types of matter; and (iii) other SCHS fields.
Date: Friday 1 April, 2022
Title: D-brane masses and periods
Abstract: Periods are special complex numbers obtained as integrals of algebraic functions over domains given by algebraic equations, each with rational coefficients. We explain the relations between periods and complex manifolds, in particular Calabi-Yau manifolds. Superstring theory compactifications on Calabi-Yau threefolds have BPS states known as D-branes. For special choices of their moduli, the masses of D-branes are determined by periods.
Date: Friday 25 Feb, 2022
Title: Toroidal Quantum Groups in Gauge and String Theories
Abstract: Toroidal quantum groups are an extension of the traditional algebraic structures describing the symmetries of quantum integrable systems. Over the past ten years, they have been essential in describing the non-perturbative properties of supersymmetric gauge theories. In this talk, I will present a brief overview of the different gauge and string theory contexts in which these structures appear, with particular emphasis on the AGT correspondence (with 2D conformal field theories) and topological strings. This connection with the topological vertex led to the development of the algebraic engineering which aims to construct gauge observables from representations of quantum groups. I will present the main achievements in this area, and the remaining challenges.
Date: Friday 5 December, 2021
Title: Holography and Irrelevant Operators
Abstract: There has been considerable recent excitement about quantum field theories deformed by the irrelevant operator TTbar. Part of the reason for excitement is that the deformed theory appears to be a new structure which is neither a local quantum field theory nor a full-fledged string theory. String theory suggests that this kind of structure appears in the holographic definition of certain spacetimes which are not asymptotically AdS. I will overview some aspects of the TTbar deformation and show how the energy formula that characterizes such theories can be reproduced from a purely gravity computation.
Date: 5th November, 2021
Title: Homogeneous string bundles
Abstract: String bundles are a categorified notion of principal bundle, motivated by cancellation of anomalies in string theory. However it is not so clear what sort of examples arise or can be constructed. This issue is compounded when one wants to write down the corresponding connections, which are valued in 2-term L-infty-algebras. I will motivate the equations the differential form data needs to satisfy, and discuss recent progress on explicit formulas for a general class of examples.
Date: Friday 26 September, 2021
Title: Calabi-Yau Metrics, CFTs and Random Matrices
Abstract: Calabi-Yau manifolds have played a key role in both mathematics and physics, and are particularly important for deriving realistic models of particle physics from string theory. Unfortunately, very little is known about the explicit metrics on these spaces, leaving us unable, for example, to compute particle masses or couplings in these models. I will review recent progress in this direction on using numerical approximations to compute the spectrum of the (p,q)-form Laplacian on these spaces. I will finish with an example of what one can do with this new "data", giving an interesting link between Calabi-Yau metrics and random matrix theory.
Date: Friday 27th August, 2021
Title: The Arithmetic of Calabi-Yau Manifolds, Black Holes and Mirror Symmetry
Abstract: The main aim of this talk is to explain that there are questions of common interest, in the context of the arithmetic of Calabi Yau 3-folds, to physicists, number theorists and geometers. The main quantities of interest, in the arithmetic context, are the numbers of points of the manifold considered as a variety over a finite field. We are interested in the computation of these numbers and their dependence on the moduli of the variety. The surprise, for a physicist, is that the numbers of points over a finite field are also given by expressions that involve the periods of a manifold. The number of points are encoded in the local zeta function, about which much is known in virtue of the Weil conjectures. I will discuss a number of topics related to the zeta function, mirror symmetry and the appearance of modularity for one parameter families of Calabi-Yau manifolds. I will report on an example for which the quartic numerator of the zeta function factorises into two quadrics at special values of the parameter, which satisfy an algebraic equation with coefficients in Q (so independent of any particular prime), and for which the underlying manifold is smooth. We note that these factorisations are due to a splitting of the Hodge structure and that these special values of the parameters are rank two black hole attractor points in the sense of type IIB supergravity. Modular groups and modular forms arise in relation to these attractor points. To our knowledge, the rank two attractor points that were found by the application of these number theoretic techniques, provide the first explicit examples of such points for Calabi-Yau manifolds of full SU(3) holonomy. Many interesting identities follow from this identification of a rank two attractor point, some of these lead to intriguing identities for the mirror manifold. This talk reports on joint work with Mohamed Elmi, Xenia de la Ossa and Duco van Straten.
Date: Friday 28 May, 2021
Title: Thin surfaces and finite-index subfactors in chiral conformal field theory Abstract: In this talk I will discuss two approaches to axiomatizing 2d chiral conformal field theory (CFT), vertex operator algebras (VOAs) and conformal nets. While VOAs axiomatize the fields of a CFT, the conformal nets axiomatize observables localized in regions of space time. The two approaches are expected to be equivalent modulo mild hypotheses, but only partial results exist to that effect. I will discuss how to use Segal's geometric approach to field theories to interpolate between the two settings, ultimately realizing conformal nets as a "boundary value" of VOAs via the geometry of "thin surfaces." As an application, I will describe how this idea was used to apply powerful results in the theory of VOAs (Huang's rigidity theorem) to resolve open questions in the theory of finite-index subfactors pioneered by Vaughan Jones.
Date: Friday 30 April, 2021, 4pm AEST
Title: T-Duality, Witten Gerbe Modules and Jacobi Forms
Abstract: We begin by repackaging T-duality for circle bundles in an H-flux as an elegant graded analog, with an Euler operator playing a pivotal role. We then extend the T-duality Hori maps, inducing isomorphisms of twisted cohomologies on T-dual circle bundles, to graded Hori maps and show that they induce isomorphisms of two-variable series of twisted cohomologies on the T-dual circle bundles, preserving Jacobi form properties. The composition of the graded Hori map with its dual equals the Euler operator. We also construct Witten gerbe modules arising from gerbe modules and show that their graded twisted Chern characters are Jacobi forms under an anomaly vanishing condition on gerbe modules, thereby giving interesting examples of our construction. This talk is based on joint work with Fei Han (NUS).
Date: Friday 12 March, 2021, 4pm AEDT
Title: Entanglement, dualities and symmetry protected topological phases of quantum matter
Abstract: Recent years have seen tremendous advances in the description of strongly correlated topological phases of matter using tools from quantum information theory such as matrix product states (MPS) and projected entangled pairs states (PEPS). In the talk I will outline the physical ideas underlying these concepts and how they can be used to extract topological information. If time permits, I will briefly comment on own work on the topological classification of spin chains that are invariant under SU(N) rotations and the quantum group SO_q(3), respectively. In the latter case we will also exhibit unexpected relations to dualities.
Date: Friday 4th December, 2020, 4pm AEDT
Title: The Nappi-Witten model as a logarithmic CFT
Abstract: In 1993, Nappi and Witten introduced a toy model for strings propagating in an extremely simple non-flat gravitational background. As a CFT, this model corresponds to a Wess-Zumino-Witten theory in which the target space Lie group is not reductive. Here, I'll discuss some work with my former student Will Stewart on understanding the irreducible representations that one would expect to contribute to the bulk partition function. However, we also found reducible but indecomposable representations, suggesting that the Nappi-Witten model is actually a logarithmic CFT.
Date: Friday 13 November, 2020, 4pm AEDT,
Title: T-duality - a pedagogical introduction
Abstract: In this talk I will review a geometric analogue of the Fourier transform, which arises in String Theory under the name of T-duality. In particular, I will discuss global aspects of T-duality and mention some recent generalisations. T-duality has important applications in different areas of mathematics, such as in differential geometry, algebraic topology, operator algebras, noncommutative geometry, as well as in physics.
Date: Friday 2nd October, 2020, 4pm AEST
Title: Spectral aspects of topological matter with an eye on strings.
Abstract: The most important feature of topological phases of matter is that they have complementary spectrally determined properties in the bulk and on the boundary, inextricable from one another. I will explain how this is a physical manifestation of K-theory and index theory, using three experimentally verified examples: quantum Hall Hamiltonian, Weyl Hamiltonian, and mod-2 topological insulator. The index theory goes beyond what is usually used in strings, and should have new applications for the latter.
Last updated: April 2022