Balt C. van Rees
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View article: Constraining glueball couplings
Constraining glueball couplings Open
We set up a numerical S-matrix bootstrap problem to rigorously constrain bound-state couplings given by the residues of poles in elastic amplitudes. We extract upper bounds on these couplings that follow purely from unitarity, crossing sym…
View article: Skydiving to bootstrap islands
Skydiving to bootstrap islands Open
A bstract We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of “external” parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an opt…
View article: Universality of the Microcanonical Entropy at Large Spin
Universality of the Microcanonical Entropy at Large Spin Open
We consider rigorous consequences of modular invariance for two-dimensional unitary non-rational CFTs with $$c > 1$$ . Simple estimates for the torus partition function can lead to remarkably strong results. We show in particular that…
View article: Theorems for the lightcone bootstrap
Theorems for the lightcone bootstrap Open
Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE coeff…
View article: Theorems for the Lightcone Bootstrap
Theorems for the Lightcone Bootstrap Open
Consider a conformally covariant four-point function of identical scalar operators with a discrete spectrum, a twist gap, and compatible with the unitarity conditions. We give a mathematical proof confirming that the spectrum and OPE coeff…
View article: Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class
Bootstrapping frustrated magnets: the fate of the chiral ${\rm O}(N)\times {\rm O}(2)$ universality class Open
We study multiscalar theories with $\text{O}(N) \times \text{O}(2)$ symmetry. These models have a stable fixed point in $d$ dimensions if $N$ is greater than some critical value $N_c(d)$. Previous estimates of this critical value from pert…
View article: A bootstrap study of minimal model deformations
A bootstrap study of minimal model deformations Open
A bstract For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-di…
View article: Perturbative RG flows in AdS. An étude
Perturbative RG flows in AdS. An étude Open
A bstract We discuss general properties of perturbative RG flows in AdS with a focus on the treatment of boundary conditions and infrared divergences. In contrast with flat-space boundary QFT, general covariance in AdS implies the absence …
View article: Flat-space Partial Waves From Conformal OPE Densities
Flat-space Partial Waves From Conformal OPE Densities Open
We consider the behavior of the OPE density $c(Δ,\ell)$ for conformal four-point functions in the flat-space limit where all scaling dimensions become large. We find evidence that the density reduces to the partial waves $f_\ell(s)$ of the…
View article: Perturbative RG flows in AdS: an étude
Perturbative RG flows in AdS: an étude Open
We discuss general properties of perturbative RG flows in AdS with a focus on the treatment of boundary conditions and infrared divergences. In contrast with flat-space boundary QFT, general covariance in AdS implies the absence of indepen…
View article: Skydiving to Bootstrap Islands
Skydiving to Bootstrap Islands Open
We study families of semidefinite programs (SDPs) that depend nonlinearly on a small number of "external" parameters. Such families appear universally in numerical bootstrap computations. The traditional method for finding an optimal point…
View article: Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms
Quantum Field Theory in AdS Space instead of Lehmann-Symanzik-Zimmerman Axioms Open
The boundary correlation functions for a quantum field theory (QFT) in a fixed anti-de Sitter (AdS) background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With …
View article: A bootstrap study of minimal model deformations
A bootstrap study of minimal model deformations Open
For QFTs in AdS the boundary correlation functions remain conformal even if the bulk theory has a scale. This allows one to constrain RG flows with numerical conformal bootstrap methods. We apply this idea to flows between two-dimensional …
View article: QFT in AdS instead of LSZ
QFT in AdS instead of LSZ Open
The boundary correlation functions for a QFT in a fixed AdS background should reduce to S-matrix elements in the flat-space limit. We consider this procedure in detail for four-point functions. With minimal assumptions we rigorously show t…
View article: Snowmass White Paper: S-matrix Bootstrap
Snowmass White Paper: S-matrix Bootstrap Open
The S-matrix Bootstrap originated on the idea that the S-matrix might be fully constrained by global symmetries, crossing, unitarity, and analyticity without relying on an underlying dynamical theory that may or may not be a quantum field …
View article: Bootstrapping boundary-localized interactions II: Minimal models at the boundary
Bootstrapping boundary-localized interactions II: Minimal models at the boundary Open
We provide evidence for the existence of non-trivial unitary conformal boundary conditions for a three-dimensional free scalar field, which can be obtained via a coupling to the m'th unitary diagonal minimal model. For large m we can demon…
View article: Navigator function for the conformal bootstrap
Navigator function for the conformal bootstrap Open
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information "allo…
View article: Navigator function for the conformal bootstrap
Navigator function for the conformal bootstrap Open
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded. We propose a new method for searching theory space that replaces the binary information “allo…
View article: Report on 2104.09518v1
Report on 2104.09518v1 Open
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded.We propose a new method for searching theory space that replaces the binary information "allow…
View article: Report on 2104.09518v1
Report on 2104.09518v1 Open
Current numerical conformal bootstrap techniques carve out islands in theory space by repeatedly checking whether points are allowed or excluded.We propose a new method for searching theory space that replaces the binary information "allow…
View article: Applications of alpha space
Applications of alpha space Open
We extend the definition of ‘alpha space’ as introduced in [1] to two spacetime dimensions. We discuss how this can be used to find conformal block decompositions of known functions and how to easily recover several lightcone bootstrap res…
View article: Landau diagrams in AdS and S-matrices from conformal correlators
Landau diagrams in AdS and S-matrices from conformal correlators Open
A bstract Quantum field theories in AdS generate conformal correlation functions on the boundary, and in the limit where AdS is nearly flat one should be able to extract an S-matrix from such correlators. We discuss a particularly simple p…
View article: The S-matrix bootstrap IV: multiple amplitudes
The S-matrix bootstrap IV: multiple amplitudes Open
We explore the space of consistent three-particle couplings in ℤ2-symmetric two-dimensional QFTs using two first-principles approaches. Our first approach relies solely on unitarity, analyticity and crossing symmetry of the two-to-two scat…
View article: Counterterms in Truncated Conformal Perturbation Theory
Counterterms in Truncated Conformal Perturbation Theory Open
We investigate the perturbative renormalisation of deformed conformal field theories from the Hamiltonian perspective. We discuss the relation with conformal perturbation theory, to which we provide an explicit match up to third order in t…
View article: The S-matrix bootstrap. Part I: QFT in AdS
The S-matrix bootstrap. Part I: QFT in AdS Open
We propose a strategy to study massive Quantum Field Theory (QFT) using conformal bootstrap methods. The idea is to consider QFT in hyperbolic space and study correlation functions of its boundary operators. We show that these are solution…