Related papers: Dispersive CFT Sum Rules
These lecture notes give a pedagogical introduction to the use of dispersion relations in loop calculations. We first derive dispersion relations which allow us to recover the real part of a physical amplitude from the knowledge of its…
We use a dispersion relation in conjunction with the operator product expansion (OPE) to derive model independent sum rules for the dynamic structure functions of systems with large scattering lengths. We present an explicit sum rule for…
We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in different…
A reanalysis of collinear factorization for inclusive Deep Inelastic Scattering shows that a novel, non perturbative spin-flip term associated with the invariant mass of the produced hadrons couples, at large enough Bjorken $x_B$, to the…
We explore the properties of two-point cosmic propagators when Perturbation Theory (PT) loop corrections are consistently taken into account. We show in particular how the interpolation scheme proposed in arXiv:1112.3895 can be explicitly…
Models for double parton distributions that are realistic and consistent with theoretical constraints are crucial for a reliable description of double parton scattering. We show how an ansatz that has the correct behaviour in the limit of…
Motivated by the normal state of the cuprates in which the f-sum rule increases faster than a linear function of the particle density, we derive a conductivity sum rule for a system in which the kinetic energy operator in the Hamiltonian is…
We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are…
We review a framework for the conformal bootstrap that does not rely on positivity and treats the infinite tower of high-dimension OPE contributions to conformal correlators through dispersion relations and neural networks. We apply it to…
In these lectures we provide a basic introduction into the topic of dispersion relation and analyticity. The properties of 2-point functions are discussed in some detail from the viewpoint of the K\"all\'en-Lehmann and general dispersion…
We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…
We discuss the constraints that a conformal field theory should enjoy to admit exactly marginal deformations, i.e. to be part of a conformal manifold. In particular, using tools from conformal perturbation theory, we derive a sum rule from…
The determination of twist-4 corrections to the structure functions of polarized $e(\mu)N$ scattering by QCD sum rules is reviewed and critically analyzed. It is found that in the case of the Bjorken sum rule the twist-4 correction is small…
Two new QCD sum rules for nucleon tensor charge are derived from a mixed correlator of spin-1/2 and spin-3/2 nucleon interpolating fields. These sum rules are analyzed along with a sum rule obtained from the usual correlator of a general…
We consider sum rules of the Weinberg type at zero and nonzero temperatures. On the basis of the operator product expansion at zero temperature we obtain a new sum rule which involves the average of a four-quark operator on one side and…
Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation…
We rigorously apply the sum rules to the sum-over-states expression to calculate the fundamental limits of the dispersion of the two-photon absorption cross-section. A comparison of the theory with the data suggests that the truncated sum…
As the theory is subject to a section condition, coordinates in double field theory do not represent physical points in an injective manner. We argue that a physical point should be rather one-to-one identified with a `gauge orbit' in the…
We derive two sum rules by studying the low energy Compton scattering on a target of arbitrary (nonzero) spin j. In the first sum rule, we consider the possibility that the intermediate state in the scattering can have spin |j \pm 1| and…
Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing $N_v$ fermion species of equal masses, we next…