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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Navigator function for the conformal bootstrap

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 "allowed"/"excluded" with a continuous "navigator" function that is negative in the allowed region and positive in the excluded region. Such a navigator function allows one to efficiently explore high-dimensional parameter spaces and smoothly sail towards any islands they may contain. The specific functions we introduce have several attractive features: they are well-defined in large regions of parameter space, can be computed with standard methods, and evaluation of their gradient is immediate due to an SDP gradient formula that we provide. The latter property allows for the use of efficient quasi-Newton optimization methods, which we illustrate by navigating towards the 3d Ising island.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Searching for gauge theories with the conformal bootstrap

Infrared fixed points of gauge theories provide intriguing targets for the modern conformal bootstrap program. In this work we provide some preliminary evidence that a family of gauged fermionic CFTs saturate bootstrap bounds and can potentially be solved with the conformal bootstrap. We start by considering the bootstrap for SO( N ) vector 4-point functions in general dimension D . In the large N limit, upper bounds on the scaling dimensions of the lowest SO( N ) singlet and traceless symmetric scalars interpolate between two solutions at Δ = D/ 2 – 1 and Δ = D – 1 via generalized free field theory. In 3D the critical O ( N ) vector models are known to saturate the bootstrap bounds and correspond to the kinks approaching Δ = 1 / 2 at large N . We show that the bootstrap bounds also admit another infinite family of kinks \( {\mathcal{T}}_D \) , which at large N approach solutions containing free fermion bilinears at Δ = D – 1 from below. The kinks \( {\mathcal{T}}_D \) appear in general dimensions with a D -dependent critical N * below which the kink disappears. We also study relations between the bounds obtained from the bootstrap with SO( N ) vectors, SU( N ) fundamentals, and SU( N ) × SU( N ) bi-fundamentals. We provide a proof for the coincidence between bootstrap bounds with different global symmetries. We show evidence that the proper symmetries of the underlying theories of \( {\mathcal{T}}_D \) are subgroups of SO( N ), and we speculate that the kinks \( {\mathcal{T}}_D \) relate to the fixed points of gauge theories coupled to fermions.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Conformal bootstrap deformations

We explore the space of extremal functionals in the conformal bootstrap. By recasting the bootstrap problem as a set of non-linear equations parameterized by the CFT data, we find an efficient algorithm for converging to the extremal solution corresponding to the boundary of allowed regions in the parameter space of CFTs. Furthermore, by deforming these solutions, we demonstrate that certain solutions corresponding to known theories are continuously connected. Employing these methods, we will explore the space of non-unitary CFTs in the context of modular as well as correlation function bootstrap. In two dimensions, we show that the extremal solution corresponding to the Ising model is connected to that of the Yang-Lee minimal model. By deforming this solution to three dimensions, we provide evidence that the CFT data obtained in this way is compatible with the E-expansion for a non-unitary theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

AdS/BCFT from conformal bootstrap: construction of gravity with branes and particles

We initiate a conformal bootstrap program to study AdS 3 /BCFT 2 with heavy excitations. We start by solving the bootstrap equations associated with two-point functions of scalar/non-scalar primaries under the assumption that one-point functions vanish. These correspond to gravity with a brane and a non-spinning/spinning particle where the brane and the particle do not intersect with each other. From the bootstrap equations, we obtain the energy spectrum and the modified black hole threshold. We then carefully analyze the gravity duals and find the results perfectly match the BCFT analysis. In particular, brane self-intersections, which are usually considered to be problematic, are nicely avoided by the black hole formation. Despite the assumption to solve the bootstrap equations, one-point functions of scalar primaries can be non-zero in general. We construct the holographic dual for a non-vanishing one-point function, in which the heavy particle can end on the brane, by holographically computing the Rényi entropy in AdS/BCFT. As a bonus, we find a refined formula for the holographic Rényi entropy, which appears to be crucial to correctly reproduce the boundary entropy term. On the other hand, we explain why one-point functions of non-scalar primaries always vanish from the gravity dual. The non-sensitivity of the solution for the bootstrap equation to the boundary entropy helps us to construct gravity duals with negative tension branes. We also find a holographic dual of boundary primaries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Automorphic spectra and the conformal bootstrap

We describe a new method for constraining Laplacian spectra of hyperbolic surfaces and 2-orbifolds. The main ingredient is consistency of the spectral decomposition of integrals of products of four automorphic forms. Using a combination of representation theory of PSL 2 (R) and semidefinite programming, the method yields rigorous upper bounds on the Laplacian spectral gap. In several examples, the bound is nearly sharp. For instance, our bound on all genus-2 surfaces is λ 1 ≤ 3.8388976481, while the Bolza surface has λ 1 ≈ 3.838887258. The bounds also allow us to determine the set of spectral gaps attained by all hyperbolic 2-orbifolds. Our methods can be generalized to higher-dimensional hyperbolic manifolds and to yield stronger bounds in the two-dimensional case. The ideas were closely inspired by modern conformal bootstrap.

Kravchuk, Petr↗
DOE OSTI2022

Bootstrapping conformal QED 3 and deconfined quantum critical point

We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED 3 ) coupled to N f flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(N f ) adjoint and $SO (N^2_f-1$) vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the $SO (N^2_f-1$) symmetry, the SU(N f ) adjoint bootstrap bounds with large N f converge to the 1/N f perturbative results of QED 3 . Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED 3 is slightly above 2: $N^*_f\in$ (2,4). Bootstrap results near $N^*_f$ are well consistent with the merger and annihilation mechanism for the loss of conformality in QED 3 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Precision Computations in Strongly Coupled Conformal Field Theories (Final Technical Report)

Conformal Field Theories (CFTs) are quantum field theories that are invariant under the conformal symmetry group (which includes translations and rotations, but also local rescalings of spacetime). They are building blocks of general quantum field theories, and appear in many areas of physics, including statistical physics, condensed matter physics, particle physics, and quantum gravity. Because of their extra symmetries, the mathematical structure of CFTs is tightly constrained, and this leads to the idea of the ``conformal bootstrap," which is to use these mathematical structures to constrain, and in some cases determine, CFT observables. A new numerical implementation of the conformal bootstrap idea appeared in 2008 with the work of Rattazzi, Rychkov, Tonni, and Vichi. Their observation was that certain bootstrap constraints (conformal symmetry and unitarity) could be combined to yield a convex optimization problem that constraints CFT data. By solving this convex optimization problem on a computer, one could obtain bounds on observables like critical exponents and operator product expansion (OPE) coefficients. Over the course of this award, the PI has improved numerical bootstrap techniques by optimizing known algorithms and finding new ones for performing the required convex optimization computations. The PI has applied these techniques to compute high-precision observables in several important strongly-coupled systems. The PI has also explored both analytical and numerical bootstrap methods for constraining the space of low energy effective field theories of quantum gravity, and developed new analytical techniques for CFT and QFT more broadly.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Bootstrapping mixed correlators in three-dimensional cubic theories II

Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the \varepsilon ε expansion. In an earlier work, we used the nonperturbative numerical conformal bootstrap to provide evidence for the existence of a previously unknown 3D CFT with cubic symmetry, dubbed “Platonic CFT”. In this work, we make further use of the numerical conformal bootstrap to perform a three-dimensional scan in the space of scaling dimensions of three low-lying operators. We find a three-dimensional isolated allowed region in parameter space, which includes both the 3D (decoupled) Ising model and the Platonic CFT. The essential assumptions on the spectrum of operators used to provide the isolated allowed region include the existence of a stress-energy tensor and the irrelevance of certain operators (in the renormalization group sense).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Bootstrapping smooth conformal defects in Chern-Simons-matter theories

Abstract 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 largeNholographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, largeNfactorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.

Physics↗
DOE OSTI2020

Bootstrap bounds on closed Einstein manifolds

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Bootstrapping Mixed MN Correlators in 3D

The recent emergence of the modern conformal bootstrap method for the study of conformal field theories (CFTs) has enabled the revisiting of old problems in classical critical phenomena described by three-dimensional CFTs. The study of such CFTs with O(m)^n \rtimes S_n O ( m ) n ⋊ S n global symmetry, also known as models, is pursued in this work. Systems of mixed correlators involving scalar operators in two different representations of the global symmetry group are considered. Isolated allowed regions are found in parameter space for various values of m m and n n . These ``islands’’ can be separated into two qualitative groups: those close to the unitarity bound and those further away. As a by-product of our analysis generic tensor structures required to bootstrap any G^n \rtimes S_n G n ⋊ S n theory with G G arbitrary are worked out.

Kousvos, Stefanos Robert↗
DOE OSTI2021

3d N=4 Bootstrap and Mirror Symmetry

We investigate the non-BPS realm of 3d {N} = 4 N = 4 superconformal field theory by uniting the non-perturbative methods of the conformal bootstrap and supersymmetric localization, and utilizing special features of 3d {N} = 4 N = 4 theories such as mirror symmetry and a protected sector described by topological quantum mechanics (TQM). Supersymmetric localization allows for the exact determination of the conformal and flavor central charges, and the latter can be fed into the mini-bootstrap of the TQM to solve for a subset of the OPE data. We examine the implications of the Z_2 Z 2 mirror action for the SCFT single- and mixed-branch crossing equations for the moment map operators, and apply numerical bootstrap to obtain universal constraints on OPE data for given flavor symmetry groups. A key ingredient in applying the bootstrap analysis is the determination of the mixed-branch superconformal blocks. Among other results, we show that the simplest known self-mirror theory with SU(2) \times SU(2) S U ( 2 ) × S U ( 2 ) flavor symmetry saturates our bootstrap bounds, which allows us to extract the non-BPS data and examine the self-mirror Z_2 Z 2 symmetry thereof.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Bootstrapping closed string field theory

The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate how Strebel differentials arise from hyperbolic string vertices by performing a WKB approximation to the associated Fuchsian equation, which we subsequently use it to derive a Polyakov-like conjecture for Strebel differentials. This result implies that the string vertices are generated by the interactions of n zero momentum tachyons, or equivalently, a certain limit of suitably regularized on-shell Liouville action. We argue that the latter can be related to the interaction of three zero momentum tachyons on a generalized cubic vertex through classical conformal blocks. We test this claim for the quartic vertex and discuss its generalization to higher-string interactions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Bootstrapping the 3d Ising stress tensor

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators σ and ϵ, and the stress tensor T μν . We obtain new precise determinations of scaling dimensions (∆ σ , ∆ ϵ ) = (0.518148806(24), 1.41262528(29)) as well as OPE coefficients involving σ, ϵ, and T μν . We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.

Conformal and W Symmetry↗
DOE OSTI2021

Bootstrap and amplitudes: a hike in the landscape of quantum field theory

This article is an introduction to two currently very active research programs, the Conformal Bootstrap and Scattering Amplitudes. Rather than attempting full surveys, the emphasis is on common ideas and methods shared by these two seemingly very different programs. In both fields, mathematical and physical constraints are placed directly on the physical observables in order to explore the landscape of possible consistent quantum field theories. We give explicit examples from both programs: the reader can expect to encounter boiling water, ferromagnets, pion scattering, and emergent symmetries on this journey into the landscape of local relativistic quantum field theories. Here, the first part is written for a general physics audience. The second part includes further details, including a new on-shell bottom-up reconstruction of the CP 1 model with the Fubini-Study metric arising from re-summation of the n-point interaction terms derived from amplitudes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Discreteness and integrality in Conformal Field Theory

Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of the conformal bootstrap, but understanding of the abstract implications of discreteness and integrality for the space of CFTs is lacking. We systematically study these constraints in two-dimensional, non-holomorphic CFTs, making use of two main mathematical results. First, we prove a theorem constraining the behavior near the cusp of integral, vector-valued modular functions. Second, we explicitly construct non-factorizable, non-holomorphic cuspidal functions satisfying discreteness and integrality, and prove the non-existence of such functions once positivity is added. Application of these results yields several bootstrap-type bounds on OPE data of both rational and irrational CFTs, including some powerful bounds for theories with conformal manifolds, as well as insights into questions of spectral determinacy. We prove that in rational CFT, the spectrum of operator twists t ≥ c/12 is uniquely determined by its complement. Likewise, we argue that in generic CFTs, the spectrum of operator dimensions Δ > c–1/12 is uniquely determined by its complement, absent fine-tuning in a sense we articulate. Finally, we discuss implications for black hole physics and the (non-)uniqueness of a possible ensemble interpretation of AdS 3 gravity.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗