Scale anomalies, states, and rates in conformal field theory

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Toda conformal field theories (CFTs) form a family of two-dimensional CFTs indexed by semisimple and complex Lie algebras. One of their remarkable features is that they are natural generalizations of Liouville CFT that enjoy an enhanced level of symmetry, ...

We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassica ...

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independ ...

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in Ad ...

In this work we study families of Z(2) orbifolds of toroidal conformal field theories based on both factorizable and non-factorizable target space tori. For these classes of theories, we analyze their moduli spaces, and compute their partition functions. B ...

Quantum Field Theories are a central object of interest of modern physics, describing fundamental interactions of matter. However, current methods give limited insight into strongly coupling theories. S-matrix bootstrap program, described in this thesis, a ...

We study the renormalization group flow of unitary Quantum Field Theories on two-dimensional de Sitter (dS) spacetime. We prove the existence of two functions of the radius of dS that interpolate between the central charges of the UV and IR fixed points of ...

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetri ...

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

Within the AdS/CFT correspondence, we identify a class of CFT operators which represent diff-invariant and approximately local observables in the gravitational dual. Provided that the bulk state breaks all asymptotic symmetries, we show that these operator ...

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Kallen-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we ...

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing nature. The o ...

In this Letter, we address the question of whether the conformal invariance can be considered as a global symmetry of a theory of fundamental interactions. To describe Nature, this theory must contain a mechanism of spontaneous breaking of the scale symmet ...

We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar quasiprimary operators (i.e. phi x phi) implies the existence of a family of quasiprimary operators O t,l with spins l ->.infinity and twi ...

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning l ...

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

We expand Hilbert series technologies in effective field theory for the inclusion of massive particles, enabling, among other things, the enumeration of operator bases for non-linearly realized gauge theories. We find that the Higgs mechanism is manifest a ...

We use numerical bootstrap techniques to study correlation functions of traceless sym-metric tensors of O(N) with two indices ti j. We obtain upper bounds on operator dimen-sions for all the relevant representations and several values of N. We discover sev ...

Scale anomalies, states, and rates in conformal field theory

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Three-point correlation functions in the $\mathfrak{sl}_{3}$ Toda theory II: The Fateev–Litvinov formula

Flux correlators and semiclassics

Null energy constraints on two-dimensional RG flows

Bootstrapping smooth conformal defects in Chern-Simons-matter theories

Ensemble averages of Z2 orbifold classes of Narain CFTs

Bootstrapping amplitudes of scalar particles

RG flows in de Sitter: C-functions and sum rules

Impossible symmetries and conformal gravity

On the Generalization of Stochastic Gradient Descent with Momentum

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Anomalous and Chern topological waves in hyperbolic networks

Holography and localization of information in quantum gravity

The Källén-Lehmann representation in de Sitter spacetime

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

Anomaly-free scale symmetry and gravity

Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap

Identifying Large Charge operators

Nonperturbative aspects of scattering amplitudes

Hilbert series, the Higgs mechanism, and HEFT

Bootstrapping traceless symmetric O(N) scalars