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We compute the sphere and disk partition functions in semiclassical Liouville and analogous quantities in double-scaled matrix integrals. The quantity sphere/disk2 is unambiguous and we find a precise numerical match between the Liouville answer and the matrix integral answer. An application is to show that the sphere partition function in JT gravity is infinite.
We initiate the study of supersymmetry-preserving topological defect lines (TDLs) in the Conway moonshine module V f♮ . We show that the tensor category of such defects, under suitable assumptions, admits a surjective but non-injective ring homomorphism into the ring of $\mathbb{Z}$-linear maps of the Leech lattice into itself. This puts strong constraints on possible defects and their quantum dimensions. We describe a simple construction of non-invertible TDLs from orbifolds of holomorphic (super)vertex operator algebras, which yields non-trivial examples of TDLs satisfying our main theorem. We conjecture a correspondence between four-plane-preserving TDLs in V f♮ and supersymmetry-preserving TDLs in K3 non-linear sigma models, which extends the correspondence between symmetry groups to the level of tensor category symmetry. We establish evidence for this conjecture by constructing non-invertible TDLs in special K3 non-linear sigma models.
We discuss entanglement entropies in 4d interface CFTs based on 4d $ \mathcal{N} $ = 4 SYM coupled to 3d $ \mathcal{N}$ = 4 degrees of freedom localized on an interface. Focusing on the entanglement between the two half spaces to either side of the interface, we show that applying the Ryu-Takayanagi prescription in general leads to multiple natural entangle- ment entropies. We interpret the different entropies as corresponding to different ways of assigning the 3d degrees of freedom localized on the interface to the two half spaces. We contrast these findings with recent discussions of universal relations for entanglement entropies in 2d interface CFTs and formulate generalized relations for 4d interface CFTs which incorporate our results.
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Current theories of fundamental physics are based on quantum field theory, unifying quantum mechanics and special relativity. A similar unification of quantum field theory with gravity has been elusive. String theory is a consistent model of quantum gravity and it is important to identify general lessons that can be applied to the real world. The main technique that emerged from such studies has been the gravitational path integral. During the period of this grant, the PI has explored the implication of the gravitational path integral in novel setups to uncover new features of rotating black holes in four dimensions, as well as increasing our understanding of some specific black holes in string theory.
Superstring flux compactifications can stabilize all moduli while leading to an enormous number of vacua solutions, each leading to different 4−d laws of physics. While the string landscape provides at present the only plausible explanation for the size of the cosmological constant, it may also predict the form of weak scale supersymmetry which is expected to emerge. Rather general arguments suggest a power-law draw to large soft terms, but these are subject to an anthropic selection of a not-too-large value for the weak scale. The combined selection allows one to compute relative probabilities for the emergence of supersymmetric models from the landscape. Models with weak scale naturalness appear most likely to emerge since they have the largest parameter space on the landscape. For finetuned models such as high-scale SUSY or split SUSY, the required weak scale finetuning shrinks their parameter space to tiny volumes, making them much less likely to appear compared to natural models. Probability distributions for sparticle and Higgs masses from natural models show a preference for Higgs mass mh∼125 GeV, with sparticles typically beyond the present LHC limits, in accord with data. From these considerations, we briefly describe how natural SUSY is expected to be revealed at future LHC upgrades. This article is a contribution to the Special Edition of the journal Entropy, honoring Paul Frampton on his 80th birthday.
String theory realisations of the QCD axion are often said to belong to the anthropic window where the decay constant is around the GUT scale and the initial misalignment angle has to be tuned close to zero. In this paper we revisit this statement by studying the statistics of axion physics in the string landscape. We take moduli stabilisation properly into account since the stabilisation of the saxions is crucial to determine the physical properties of the corresponding axionic partners. We focus on the model-independent case of closed string axions in type IIB flux compactifications and find that their decay constants and mass spectrum feature a logarithmic, instead of a power-law, distribution. In the regime where the effective field theory is under control, most of these closed string axions are ultra-light axion-like particles, while axions associated to blow-up modes can naturally play the role of the QCD axion. Hence, the number of type IIB flux vacua with a closed string QCD axion with an intermediate scale decay constant and a natural value of the misalignment angle is only logarithmically suppressed. In a recent paper we found that this correlates also with a logarithmic distribution of the supersymmetry breaking scale, providing the intriguing indication that most, if not all, of the phenomenologically interesting quantities in the string landscape might feature a logarithmic distribution.
The project involved an integrated program of research which focused on the use of the extra-dimensional geometry of string theory as a tool in understanding a variety of phenomena in quantum field theory. This was used to construct and study new examples of quantum field theories with the eventual aim of also using these results to develop new particle physics and cosmology scenarios. The research involved the development of new methods for constructing such extra-dimensional geometries, and also the study of the resulting quantum field theories generated by this process.
We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor scalar charge theory. This work is motivated by questions of the relationship between fracton phases and continuum quantum field theories, and also provides general principles to describe p-string condensation independent of specific lattice model constructions. We give a perspective on higher-form symmetry in lattice models in terms of cellular homology. Applying this perspective to the coupled-layer construction of the X-cube model, we identify a foliated 1-form symmetry that is broken in the X-cube phase, but preserved in the phase of decoupled toric code layers. Similar considerations for the scalar charge theory lead to a framed 1-form symmetry. These symmetries are distinct from standard 1-form symmetries that arise, for instance, in relativistic quantum field theory. Here, we also give a general discussion on interpreting p-string condensation, and related constructions involving gauging of symmetry, in terms of higher-form symmetry.
Understanding the dynamics of bound state formation is one of the fundamental questions in confining quantum field theories such as Quantum Chromodynamics (QCD). One hadronization mechanism that has garnered significant attention is the breaking of a string initially connecting a fermion and an antifermion. Deepening our understanding of real-time string-breaking dynamics with simpler, lower dimensional models like the Schwinger model can improve our understanding of the hadronization process in QCD and other confining systems found in condensed matter and statistical systems. Here in this paper, we consider the string-breaking dynamics within the Schwinger model and investigate its modification inside a thermal medium, treating the Schwinger model as an open quantum system coupled to a thermal environment. Within the regime of weak coupling between the system and environment, the real-time evolution of the system can be described by a Lindblad evolution equation. We analyze the Liouvillian gaps of this Lindblad equation and the time dependence of the system’s von Neumann entropy. We observe that the late-time relaxation rate decreases as the environment correlation length increases. Moreover, when the environment correlation length is infinite, the system exhibits two steady states, one in each of the sectors with definite charge-conjugation-parity (CP) quantum numbers. For parameter regimes where an initial string breaks in vacuum, we observe a delay of the string breaking in the medium, due to kinetic dissipation effects. Conversely, in regimes where an initial string remains intact in vacuum time evolution, we observe string breaking (melting) in the thermal medium. We further discuss how the Liouvillian dynamics of the open Schwinger model can be simulated on quantum computers and provide an estimate of the associated Trotter errors.
We define and compute the leading sphere diagram contribution to the entropy of the BTZ black hole supported by Kalb-Ramond flux in bosonic string theory. In a winding condensate description, integrating exactly over the constant mode for the radial direction of AdS 3 reduces the problem to one of the correlation functions of winding operators in the free theory. The volume of the residual PSL(2,ℂ) gauge group of the sphere is canceled by the action of conformal transformations on the winding interaction insertions. We formulate a precise version of the replica trick in terms of (infinitesimally) non-integer winding condensates to produce the entropy of the BTZ black hole. The resulting entropy can be calculated from the one-point function of a non-local operator on the worldsheet.
AdS 3 string theory in the stringy regime k = (R AdS /ℓ s ) 2 < 1 provides a laboratory for the study of holography in which both sides of AdS/CFT duality are under fairly good control. Worldsheet string theory is solvable, and for closed strings the dual spacetime CFT is a deformation of a symmetric product orbifold. Here we extend this construction to include open strings by adding a probe D-string, described semiclassically by an AdS 2 D-brane in AdS 3 . The dual defect or boundary conformal field theory (BCFT) is again a deformed symmetric product, which now describes the Fock space of long open and closed strings near the AdS boundary, with a boundary deformation implementing the open/closed transition in addition to the symmetric product $\mathbb{Z}$ 2 twist deformation that implements closed string joining/splitting. The construction thus provides an explicit example of an AdS 3 /BCFT 2 duality.
We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit. The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T 9/5 . We also present a similar argument for all other Dp-brane geometries. We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an Ad S2+9/5 × S 8 geometry.
We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the “KLT algebra” and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy in addition to locality constraints. We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a ‘heterotic’-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order ∇ 10 R 4 . Finally, we initiate a search for new double-copy kernels.
Quantum field theory is a unifying language that pervades many areas of modern physics. The project revolves around the study of strongly-coupled quantum field theories that are not amenable to conventional perturbative techniques – with a particular focus on strongly- coupled gauge theories.
The emerging study of fractons, a new type of quasi-particle with restricted mobility, has motivated the construction of several classes of interesting continuum quantum field theories with novel properties. One such class consists of foliated field theories which, roughly, are built by coupling together fields supported on the leaves of foliations of spacetime. Another approach, which we refer to as exotic field theory, focuses on constructing Lagrangians consistent with special symmetries (like subsystem symmetries) that are adjacent to fracton physics. A third framework is that of infinite-component Chern-Simons theories, which attempts to generalize the role of conventional Chern-Simons theory in describing (2+1)D Abelian topological order to fractonic order in (3+1)D. The study of these theories is ongoing, and many of their properties remain to be understood. Historically, it has been fruitful to study QFTs by embedding them into string theory. One way this can be done is via D-branes, extended objects whose dynamics can, at low energies, be described in terms of conventional quantum field theory. Further, QFTs that can be realized in this way can then be analyzed using the rich mathematical and physical structure of string theory. In this paper, we show that foliated field theories, exotic field theories, and infinite-component Chern-Simons theories can all be realized on the world-volumes of branes. We hope that these constructions will ultimately yield valuable insights into the physics of these interesting field theories.
We discuss dark energy, dark matter and the hierarchy problem in the context of a general non-commutative formulation of string theory. In this framework dark energy is generated by the dynamical geometry of the dual spacetime while dark matter, on the other hand, comes from the degrees of freedom dual to the visible matter. This formulation of string theory is sensitive both to the IR and UV scales and the Higgs scale is radiatively stable by being a geometric mean of radiatively stable UV and IR scales. We also comment on various phenomenological signatures of this novel approach to dark energy, dark matter and the hierarchy problem. We find that this new view on the hierarchy problem is realized in a toy model based on a non-holomorphic deformation of the stringy cosmic string. Finally, we discuss a proposal for a new non-perturbative formulation of string theory, which sheds light on M theory and F theory, as well as on supersymmetry and holography.