Christopher M. Hull

A bstract: The action for self-dual gauge fields that emerges from the recently constructed superstring field theory is found. The new superstring field theory reduces to that of Sen in a certain limit, and in this limit the new action for self-dual gauge fields reduces to Sen’s action for such fields. The theory describes two decoupled self-dual gauge fields that couple to two metrics, with each gauge field coupling to only one of the metrics. The action also features a background metric, and the non-linear coupling to these three metrics is non-standard. There are two spin-two gauge invariances, and diffeomorphisms arise from the diagonal subgroup.

A bstract: Sen’s action in two dimensions governs a chiral boson coupled to a two-dimensional metric together with a second chiral boson that couples to a flat two-dimensional metric. This second scalar decouples from the physical degrees of freedom. The generalisation of this action to one in which the second chiral scalar couples to an arbitrary second metric is used to formulate the theory on an arbitrary two-dimensional manifold. We use this action with both metrics Riemannian (or complex) to formulate the path integral on any Riemann surface. We calculate the partition function in this way and check the result with that calculated using canonical quantisation, and then extend this to multiple chiral bosons. The partition function for chiral scalars taking values on a rational torus is a sum of terms, each of which is the product of two holomorphic functions, one a function of the modulus of the first metric and the other a function of the modulus of the second metric. In particular, for the case of chiral bosons moving on a torus defined by an even self-dual lattice, the partition function is a single product of two such holomorphic functions, not a sum of such terms. This is applied to the heterotic string to give a world-sheet action whose quantisation is modular invariant and free from anomalies. We discuss modular invariance for the moduli of both metrics and the extension to higher genus Riemann surfaces.

We study the role of categorical symmetries in constraining the renormalization of couplings in two-dimensional nonlinear sigma models with a Wess-Zumino term. A large class of these theories admits self-duality symmetries associated with discrete gauging and T-duality. They are generically nonconformal, but we argue that a particular coupling is protected from quantum corrections by the categorical symmetry. We give strong evidence for this claim by showing that the β -function for this coupling vanishes to 2-loop order if and only if this symmetry is present. Furthermore, in cases where the target space is a group manifold, the nonrenormalization result can be proven to hold nonperturbatively.

A bstract: We formulate interacting antisymmetric tensor gauge theory in a configuration space consisting of a pair of dual field strengths which has a natural symplectic structure. The field equations are formulated as the intersection of a pair of submanifolds of this infinite-dimensional symplectic configuration space, one of which is a Lagrangian submanifold while the other is either a coisotropic or Lagrangian submanifold, depending on the topology. Chern-Simons interactions give the configuration space an interesting global structure. We consider in detail the example of a six-dimensional theory of a 3-form field strength coupled to Yang-Mills theory via a Chern-Simons interaction. Our approach applies to a broad class of gauge systems.

We construct a set of higher-form conserved currents on spacetimes admitting conformal Killing–Yano tensors. We find relations between these currents that allow the charge given by integrating one of these currents over a region to be re-expressed as an integral of a covariant quantity over the boundary. In many cases, only a non-covariant form of the boundary integral was previously known. For a special class of these currents the conservation does not rely on field equations, so they give conserved topological charges in any gravitational theory. We discuss the relation of our currents to the Komar current and derive several new properties of conformal Killing–Yano tensors. We study a number of applications of our construction to charges of black hole solutions of Einstein–Maxwell theory, and D-brane solutions of type II supergravity.

A bstract: Sen’s action for chiral bosons in 2 dimensions describes two chiral scalars, one of which couples to the physical metric and one of which couples to a flat metric. It has a generalisation in which the flat metric is replaced by an arbitrary second metric and so can be formulated on any curved world-sheet. When the two metrics are equal, the theory reduces to a βγ system, giving a non-unitary c = 2 conformal field theory. We argue that the relation between this and the theory of two chiral bosonic scalars of the same chirality can be viewed as a ‘bosonisation’. We show that the standard vertex operators for the chiral scalars are vertex operators and line operators in the Sen formulation and derive the formulation in the Sen theory of correlation functions in the chiral scalar theory. The flat space Sen theory can be coupled to two different world-sheet metrics in such a way that one scalar couples to one metric and the other to the other metric, so obtaining the general formulation with two metrics. In d = 4 k + 2 dimensions, the bi-metric action for a 2 k -form gauge field with self-dual field strength reduces, when the two metrics are equal, to a conformal field theory with a BF -type action, except that B is a self-dual d /2-form and F is a d /2-form field strength, F = dP . The self-duality of B means that this is not a topological theory but instead represents two self-dual gauge fields. This has a generalisation to a democratic action for p -form gauge fields in any dimension.

Global symmetries can be generalised to transformations generated by topological operators, including cases in which the topological operator does not have an inverse. A family of such topological operators are intimately related to dualities via the procedure of half-space gauging. In this work we discuss the construction of non-invertible defects based on T-duality in two dimensions, generalising the well-known case of the free compact boson to any Non-Linear Sigma Model with Wess-Zumino term which is T-dualisable. This requires that the target space has an isometry with compact orbits that acts without fixed points. Our approach allows us to include target spaces without non-trivial 1-cycles, does not require the NLSM to be conformal, and when it is conformal it does not need to be rational; moreover, it highlights the microscopic origin of the topological terms that are responsible for the non-invertibility of the defect. An interesting class of examples are Wess-Zumino-Witten models, which are self-dual under a discrete gauging of a subgroup of the isometry symmetry and so host a topological defect line with Tambara-Yamagami fusion. Along the way, we discuss how the usual 0-form symmetries match across T-dual models in target spaces without 1-cycles, and how global obstructions can prevent locally conserved currents from giving rise to topological operators.

We study the role of categorical symmetries in constraining the renormalisation of couplings in two-dimensional non-linear sigma models with Wess-Zumino term. A large class of these theories admit self-duality symmetries associated with discrete gauging and T-duality. They are generically non-conformal, but we argue that a particular coupling is protected from quantum corrections by the categorical symmetry. We give strong evidence for this claim by showing that the $β$-function for this coupling vanishes to 2-loop order if and only if this symmetry is present. Furthermore, in cases where the target space is a group manifold, the non-renormalisation result can be proven to hold non-perturbatively.

We use freely acting asymmetric orbifolds of type IIB string theory to construct a class of theories in four dimensions with eight supercharges. Their low energy effective field theories resemble STU models, but have different duality groups: the orbifold’s free action reduce the duality groups to congruence subgroups of the modular group. The fundamental domain is consequently larger and contains new interesting points at infinite distance on the real axis bounding the upper half plane. We verify that the distance conjectures hold in the non-geometric compactification of string theory studied here. In particular, we find points at infinite distance in moduli space at which the theory decompactifies to a different orbifold construction.

Dirac’s formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities associated with the Dirac strings. The field equations of Dirac’s theory do not depend on the positions of the Dirac strings provided that they do not intersect the worldlines of any electrically charged particles; this constraint is called the Dirac veto. It is shown that Dirac’s action is independent of the positions of the Dirac strings and that this corresponds to a local 1-form symmetry. The electric and magnetic 1-form symmetries have a mixed anomaly, and the Dirac veto is shown to correspond to a restriction to gauge transformations for which the anomaly vanishes. The extension to p-form gauge fields in d-dimensions coupled to charged branes is discussed, together with the possibility of cancelling the anomaly by embedding in a higher-dimensional theory and so avoiding the veto.