The S-matrix bootstrap. Part I: QFT in AdS Paulos, Miguel F.; Penedones, Joao; Toledo, Jonathan ...
The journal of high energy physics,
11/2017, Letnik:
2017, Številka:
11
Journal Article
Recenzirano
Odprti dostop
A
bstract
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 solutions of the crossing equations in one lower dimension. By sending the curvature radius of the background hyperbolic space to infinity we expect to recover flat-space physics. We explain that this regime corresponds to large scaling dimensions of the boundary operators, and discuss how to obtain the flat-space scattering amplitudes from the corresponding limit of the boundary correlators. We implement this strategy to obtain universal bounds on the strength of cubic couplings in 2D flat-space QFTs using 1D conformal bootstrap techniques. Our numerical results match precisely the analytic bounds obtained in our companion paper using S-matrix bootstrap techniques.
A
bstract
In 1, 2 we proposed an approach based on graphs to characterize 5d superconformal field theories (SCFTs), which arise as compactifications of 6d
N
= (1
,
0) SCFTs. The graphs, so-called ...combined fiber diagrams (CFDs), are derived using the realization of 5d SCFTs via M-theory on a non-compact Calabi-Yau threefold with a canonical singularity. In this paper we complement this geometric approach by connecting the CFD of an SCFT to its weakly coupled gauge theory or quiver descriptions and demonstrate that the CFD as recovered from the gauge theory approach is consistent with that as determined by geometry. To each quiver description we also associate a graph, and the embedding of this graph into the CFD that is associated to an SCFT provides a systematic way to enumerate all possible consistent weakly coupled gauge theory descriptions of this SCFT. Furthermore, different embeddings of gauge theory graphs into a fixed CFD can give rise to new UV-dualities for which we provide evidence through an analysis of the prepotential, and which, for some examples, we substantiate by constructing the M-theory geometry in which the dual quiver descriptions are manifest.
A
bstract
We compute the scattering amplitude for classical black-hole scattering to third order in the Post-Minkowskian expansion, keeping all terms needed to derive the scattering angle to that ...order from the eikonal formalism. Our results confirm a conjectured relation between the real and imaginary parts of the amplitude by Di Vecchia, Heissenberg, Russo, and Veneziano, and are in agreement with a recent computation by Damour based on radiation reaction in general relativity.
A
bstract
We describe a systematic framework for computing the conservative potential of a compact binary system using modern tools from scattering amplitudes and effective field theory. Our approach ...combines methods for integration and matching adapted from effective field theory, generalized unitarity, and the double-copy construction, which relates gravity integrands to simpler gauge-theory expressions. With these methods we derive the third post-Minkowskian correction to the conservative two-body Hamiltonian for spinless black holes. We describe in some detail various checks of our integration methods and the resulting Hamiltonian.
Extremal correlators and random matrix theory Grassi, Alba; Komargodski, Zohar; Tizzano, Luigi
The journal of high energy physics,
04/2021, Letnik:
2021, Številka:
4
Journal Article
Recenzirano
Odprti dostop
A
bstract
We study the correlation functions of Coulomb branch operators of four-dimensional
N
= 2 Superconformal Field Theories (SCFTs). We focus on rank-one theories, such as the SU(2) gauge theory ...with four fundamental hypermultiplets. “Extremal” correlation functions, involving exactly one anti-chiral operator, are perhaps the simplest nontrivial correlation functions in four-dimensional Quantum Field Theory. We show that the large charge limit of extremal correlators is captured by a “dual” description which is a chiral random matrix model of the Wishart-Laguerre type. This gives an analytic handle on the physics in some particular excited states. In the limit of large random matrices we find the physics of a non-relativistic axion-dilaton effective theory. The random matrix model also admits a ’t Hooft expansion in which the matrix is taken to be large and simultaneously the coupling is taken to zero. This explains why the extremal correlators of SU(2) gauge theory obey a nontrivial double scaling limit in states of large charge. We give an exact solution for the first two orders in the ’t Hooft expansion of the random matrix model and compare with expectations from effective field theory, previous weak coupling results, and we analyze the non-perturbative terms in the strong ’t Hooft coupling limit. Finally, we apply the random matrix theory techniques to study extremal correlators in rank-1 Argyres-Douglas theories. We compare our results with effective field theory and with some available numerical bootstrap bounds.
A
bstract
A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical ...scattering of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field
h
μν
(
x
) and position
x
i
μ
τ
i
of each black hole on equal footing. Using these both the 3PM three-body gravitational radiation 〈
h
μv
(
k
)〉 and 2PM two-body deflection
Δ
p
i
μ
from classical black hole scattering events are obtained. The latter can also be obtained from the eikonal phase of a 2
→
2 scalar S-matrix, which we show corresponds to the free energy of the WQFT.
A
bstract
The boundary correlation functions for a Quantum Field Theory (QFT) in an Anti-de Sitter (AdS) background can stay conformally covariant even if the bulk theory undergoes a renormalization ...group (RG) flow. Studying such correlation functions with the numerical conformal bootstrap leads to non-perturbative constraints that must hold along the entire flow. In this paper we carry out this analysis for the sine-Gordon RG flows in AdS
2
, which start with a free (compact) scalar in the UV and end with well-known massive integrable theories that saturate many S-matrix bootstrap bounds. We numerically analyze the correlation functions of both breathers and kinks and provide a detailed comparison with perturbation theory near the UV fixed point. Our bounds are often saturated to one or two orders in perturbation theory, as well as in the flat-space limit, but not necessarily in between.
A
bstract
The Hilbert space of a quantum system with internal global symmetry
G
decomposes into sectors labelled by irreducible representations of
G
. If the system is chaotic, the energies in each ...sector should separately resemble ordinary random matrix theory. We show that such “sector-wise” random matrix ensembles arise as the boundary dual of two- dimensional gravity with a
G
gauge field in the bulk. Within each sector, the eigenvalue density is enhanced by a nontrivial factor of the dimension of the representation, and the ground state energy is determined by the quadratic Casimir. We study the consequences of ’t Hooft anomalies in the matrix ensembles, which are incorporated by adding specific topological terms to the gauge theory action. The effect is to introduce projective representations into the decomposition of the Hilbert space. Finally, we consider ensembles with
G
symmetry and time reversal symmetry, and analyze a simple case of a mixed anomaly between time reversal and an internal ℤ
2
symmetry.
A Logic for Locally Complete Abstract Interpretations Bruni, Roberto; Giacobazzi, Roberto; Gori, Roberta ...
2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS),
2021-June-29
Conference Proceeding
Odprti dostop
We introduce the notion of local completeness in abstract interpretation and define a logic for proving both the correctness and incorrectness of some program specification. Abstract interpretation ...is extensively used to design sound-by-construction program analyses that over-approximate program behaviours. Completeness of an abstract interpretation A for all possible programs and inputs would be an ideal situation for verifying correctness specifications, because the analysis can be done compositionally and no false alert will arise. Our first result shows that the class of programs whose abstract analysis on A is complete for all inputs has a severely limited expressiveness. A novel notion of local completeness weakens the above requirements by considering only some specific, rather than all, program inputs and thus finds wider applicability. In fact, our main contribution is the design of a proof system, parameterized by an abstraction A, that, for the first time, combines over- and under-approximations of program behaviours. Thanks to local completeness, in a provable triple ⊢ A P c Q, the assertion Q is an under-approximation of the strongest post-condition postc(P ) such that the abstractions in A of Q and postc(P ) coincide. This means that Q is never too coarse, namely, under mild assumptions, the abstract interpretation of c does not yield false alerts for the input P iff Q has no alert. Thus, ⊢ A P c Q not only ensures that all the alerts raised in Q are true ones, but also that if Q does not raise alerts then c is correct.
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