Is CP a gauge symmetry?

Discrete gauge symmetries in global intersecting D-brane models constrain the exact form of the perturbative as well as non-perturbative superpotential. We derive the complete set of conditions on the existence of discrete Zn gauge symmetries on toroidal orbifolds, T6/Z(N) and T6/Z(2)xZ(2M}, with fractional or rigid D6-branes on tilted tori, for which global models of particle physics are known. Several examples of global left-right symmetric and Pati-Salam models are presented. Some discrete `stringy' Zn symmetries are trivial from the field theory point of view, while others have not been identified before.

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle’s mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that ‘gravity is the weakest force’. Here, we take a step towards making this expectation more precise by studying ℤN and ℤ2N gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to MPl.

Discrete gauge symmetries in axionic extensions of the supersymmetric standard model

We study aspects of Heterotic/F-theory duality for compactifications with Abelian discrete gauge symmetries. We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group {mathbb{Z}}_n . Such models are obtained by studying first a specific toric set-up whose associated Heterotic vector bundle has structure group {mathbb{Z}}_n . By employing a conjectured Heterotic/F-theory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compactifications to six dimensions. We provide explicit constructions of mirror-pairs for symmetric examples with {mathbb{Z}}_2 and {mathbb{Z}}_3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in field theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stückelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of fibrations with torsional sections and those with multi-sections.

We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.

We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.

In string compactifications, frequently the anomalous U(1) gauge symmetry appears which belongs to E_8 times E_8' of the heterotic string. This anomalous U(1) gauge boson obtains mass at the compactification scale (approx 10^{18,},text {GeV}) by absorbing one pseudoscalar (corresponding to the model-independent axion) from the second rank antisymmetric tensor field B_{MN}. Below the compactification scale a global symmetry U(1)_{mathrm{anom}} results whose charge Q_mathrm{anom} is the original gauge U(1) charge. This is the most natural global symmetry, realizing the “invisible” axion. This global symmetry U(1)_{mathrm{anom}} is suitable for a flavor symmetry. In the simplest compactification model with the flipped SU(5) grand unification, all the low energy parameters are calculated in terms of the vacuum expectation values of the standard model singlets.

A class of variational schemes for the hydrodynamic-electrodynamic model of lossless free-electron gas in a quasineutral background is developed for high-quality simulations of surface plasmon polaritons. The Lagrangian density of lossless free-electron gas with a self-consistent electromagnetic field is established, and the dynamical equations with the associated constraints are obtained via a variational principle. Based on discrete exterior calculus, the action functional of this system is discretized and minimized to obtain the discrete dynamics. Newton-Raphson iteration and the biconjugate gradient stabilized method are equipped as a hybrid nonlinear-linear algebraic solver. Instead of discretizing the partial differential equations, the variational schemes have better numerical properties in secular simulations, as they preserve the discrete Lagrangian symplectic structure, gauge symmetry, and general energy-momentum density. Two numerical experiments were performed. The numerical results reproduce characteristic dispersion relations of bulk plasmons and surface plasmon polaritons, and the numerical errors of conserved quantities in all experiments are bounded by a small value after long-term simulations.

In this thesis we study landscape constructions to challenge existing swampland conjectures and extend established ones in order to expand our understanding of quantum gravity and its possible consequences for phenomenology. We construct a new class of axions in Klebanov-Strassler throats including a four-dimensional supergravity formulation. We show that the axion and associated instantons violate the axionic weak gravity conjecture in its simplest form and that the instantons consistent with it populate very coarse charge sub-lattices. Based on the winding scenario, we show that light axionic directions of field space can posses tunable, positive minima in their scalar potential. This gives a controlled supersymmetry-breaking and uplifting mechanism which may be applied in known AdS vacua. We discuss stability of these solutions. We propose a bound on the quality of global symmetries that are derived from gauge symmetries. This involves a Stuckelberg axion as well as instantons coupling to it. Integrating over instanton insertions leads to global-symmetry-violating operators. Using the axionic weak gravity conjecture the coefficient of the operator may be bounded from below. In the spirit of the weak gravity conjecture, we constrain attractive forces in the absence of gauge charges. We claim that the minimal size of a bound state is governed by gravitational forces alone and arrive at a bound state conjecture: In an EFT, there is a universal lower bound on the typical radius of any bound state.

Superheavy Dark Matter with Discrete Gauge Symmetries

We investigate the modular transformation properties of observable (light) fields in heterotic orbifolds, in the light of recent calculations of CP-violating quantities. Measurable quantities must be modular invariant functions of string moduli, even if the light fields are noninvariant. We show that physical invariance may arise by patching smooth functions that are separately noninvariant. CP violation for <T> on the unit circle, which requires light and heavy states to mix under transformation, is allowed in principle, although the Jarlskog parameter J_CP(T) must be amended relative to previous results. However, a toy model of modular invariant mass terms indicates that the assumption underlying these results is unrealistic. In general the mass eigenstate basis is manifestly modular invariant and coupling constants are smooth invariant functions of T, thus CP is unbroken on the unit circle. We also discuss the status of CP-odd quantities when CP is a discrete gauge symmetry, and point out a link with baryogenesis.

We extend to larger unification groups an earlier study exploring the possibility of unification of gauge symmetries in theories with dynamical symmetry breaking. Based on our results, we comment on the outlook for models that seek to achieve this type of unification.

In this paper we argue for a close connection between the non-existence of global symmetries in quantum gravity and a unitary resolution of the black hole information problem. In particular we show how the essential ingredients of recent calculations of the Page curve of an evaporating black hole can be used to generalize a recent argument against global symmetries beyond the AdS/CFT correspondence to more realistic theories of quantum gravity. We also give several low-dimensional examples of quantum gravity theories which do not have a unitary resolution of the black hole information problem in the usual sense, and which therefore can and do have global symmetries. Motivated by this discussion, we conjecture that in a certain sense Euclidean quantum gravity is equivalent to holography.

Tensor network states and methods have erupted in recent years. Originally developed in the context of condensed matter physics and based on renormalization group ideas, tensor networks lived a revival thanks to quantum information theory and the understanding of entanglement in quantum many-body systems. Moreover, it has been not-so-long realized that tensor network states play a key role in other scientific disciplines, such as quantum gravity and artificial intelligence. In this context, here we provide an overview of basic concepts and key developments in the field. In particular, we briefly discuss the most important tensor network structures and algorithms, together with a sketch on advances related to global and gauge symmetries, fermions, topological order, classification of phases, entanglement Hamiltonians, AdS/CFT, artificial intelligence, the 2d Hubbard model, 2d quantum antiferromagnets, conformal field theory, quantum chemistry, disordered systems, and many-body localization.

Unlike the standard entanglement entropy considered in the holographic con- text, entwinement measures entanglement between degrees of freedom that are not associated to a spatial subregion. Entwinement is defined for two-dimensional CFTs with a discrete ℤN gauge symmetry. Since the Hilbert space of these CFTs does not factorize into tensor products, even the entanglement entropy associated to a spatial subregion cannot be defined as the von Neumann entropy of a reduced density matrix. While earlier works considered embedding the density matrix into a larger, factorizing Hilbert space, we apply a gauge invariant approach by using a density matrix uniquely defined through its relation to the local algebra of observables. We furthermore obtain a fully gauge invariant definition of entwinement valid for general CFTs with ℤN gauge symmetry in terms of all observables acting on the degrees of freedom considered. Holographically, entwinement is dual to the length of non-minimal geodesics present for conical defects or black holes. In this context, we propose a definition of entwinement for thermal states dual to the BTZ black hole. Our results show that “entwinement is enough” to describe the full bulk geometry for the conical defect and provide strong hints that the same holds true for the BTZ black hole. Thus, it provides an alternative to holographic complexity for the theories considered.