scholarly journals Towards bootstrapping RG flows: sine-Gordon in AdS

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
António Antunes ◽  
Miguel S. Costa ◽  
João Penedones ◽  
Aaditya Salgarkar ◽  
Balt C. van Rees
Keyword(s):  
Perturbation Theory ◽  
Correlation Functions ◽  
Detailed Comparison ◽  
Flat Space ◽  
Quantum Field ◽  
De Sitter ◽  
Conformal Bootstrap ◽  
S Matrix ◽  
Space Limit ◽  
Entire Flow

Abstract 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 AdS2, 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.

scholarly journals Modular invariance in superstring theory from $$ \mathcal{N} $$ = 4 super-Yang-Mills

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shai M. Chester ◽  
Michael B. Green ◽  
Silviu S. Pufu ◽  
Yifan Wang ◽  
Congkao Wen
Keyword(s):  
Partition Function ◽  
Eisenstein Series ◽  
Correlation Functions ◽  
Flat Space ◽  
Modular Invariance ◽  
Point Function ◽  
Superstring Theory ◽  
Yang Mills ◽  
S Matrix ◽  
Space Limit

Abstract We study the four-point function of the lowest-lying half-BPS operators in the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills theory and its relation to the flat-space four-graviton amplitude in type IIB superstring theory. We work in a large-N expansion in which the complexified Yang-Mills coupling τ is fixed. In this expansion, non-perturbative instanton contributions are present, and the SL(2, ℤ) duality invariance of correlation functions is manifest. Our results are based on a detailed analysis of the sphere partition function of the mass-deformed SYM theory, which was previously computed using supersymmetric localization. This partition function determines a certain integrated correlator in the undeformed $$ \mathcal{N} $$ N = 4 SYM theory, which in turn constrains the four-point correlator at separated points. In a normalization where the two-point functions are proportional to N2− 1 and are independent of τ and $$ \overline{\tau} $$ τ ¯ , we find that the terms of order $$ \sqrt{N} $$ N and $$ 1/\sqrt{N} $$ 1 / N in the large N expansion of the four-point correlator are proportional to the non-holomorphic Eisenstein series $$ E\left(\frac{3}{2},\tau, \overline{\tau}\right) $$ E 3 2 τ τ ¯ and $$ E\left(\frac{5}{2},\tau, \overline{\tau}\right) $$ E 5 2 τ τ ¯ , respectively. In the flat space limit, these terms match the corresponding terms in the type IIB S-matrix arising from R4 and D4R4 contact inter-actions, which, for the R4 case, represents a check of AdS/CFT at finite string coupling. Furthermore, we present striking evidence that these results generalize so that, at order $$ {N}^{\frac{1}{2}-m} $$ N 1 2 − m with integer m ≥ 0, the expansion of the integrated correlator we study is a linear sum of non-holomorphic Eisenstein series with half-integer index, which are manifestly SL(2, ℤ) invariant.

scholarly journals Relation between parity-even and parity-odd CFT correlation functions in three dimensions

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Sachin Jain ◽  
Renjan Rajan John
Keyword(s):  
Scattering Amplitudes ◽  
Correlation Functions ◽  
Flat Space ◽  
Three Dimensions ◽  
Higher Dimension ◽  
De Sitter ◽  
Higher Spin ◽  
Space Limit ◽  
Point Correlation

Abstract In this paper we relate the parity-odd part of two and three point correlation functions in theories with exactly conserved or weakly broken higher spin symmetries to the parity-even part which can be computed from free theories. We also comment on higher point functions.The well known connection of CFT correlation functions with de-Sitter amplitudes in one higher dimension implies a relation between parity-even and parity-odd amplitudes calculated using non-minimal interactions such as $$ {\mathcal{W}}^3 $$ W 3 and $$ {\mathcal{W}}^2\tilde{\mathcal{W}} $$ W 2 W ˜ . In the flat-space limit this implies a relation between parity-even and parity-odd parts of flat-space scattering amplitudes.

scholarly journals 6d (2, 0) and M-theory at 1-loop

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Himanshu Raj
Keyword(s):  
Flat Space ◽  
Lagrangian Description ◽  
Loop Correction ◽  
Higher Derivative ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Tensor Multiplet ◽  
First Time ◽  
M Theory

Abstract We study the stress tensor multiplet four-point function in the 6d maximally supersymmetric (2, 0) AN−1 and DN theories, which have no Lagrangian description, but in the large N limit are holographically dual to weakly coupled M-theory on AdS7× S4 and AdS7× S4/ℤ2, respectively. We use the analytic bootstrap to compute the 1-loop correction to this holographic correlator coming from Witten diagrams with supergravity R and the first higher derivative correction R4 vertices, which is the first 1-loop correction computed for a non-Lagrangian theory. We then take the flat space limit and find precise agreement with the corresponding terms in the 11d M-theory S-matrix, some of which we compute for the first time using two-particle unitarity cuts.

scholarly journals CFT unitarity and the AdS Cutkosky rules

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
David Meltzer ◽  
Allic Sivaramakrishnan
Keyword(s):  
Flat Space ◽  
Tree Level ◽  
Optical Theorem ◽  
Conformal Field Theories ◽  
Strongly Coupled ◽  
Conformal Field ◽  
Weakly Coupled ◽  
S Matrix ◽  
Space Limit ◽  
Diagrammatic Method

Abstract We derive the Cutkosky rules for conformal field theories (CFTs) at weak and strong coupling. These rules give a simple, diagrammatic method to compute the double-commutator that appears in the Lorentzian inversion formula. We first revisit weakly-coupled CFTs in flat space, where the cuts are performed on Feynman diagrams. We then generalize these rules to strongly-coupled holographic CFTs, where the cuts are performed on the Witten diagrams of the dual theory. In both cases, Cutkosky rules factorize loop diagrams into on-shell sub-diagrams and generalize the standard S-matrix cutting rules. These rules are naturally formulated and derived in Lorentzian momentum space, where the double-commutator is manifestly related to the CFT optical theorem. Finally, we study the AdS cutting rules in explicit examples at tree level and one loop. In these examples, we confirm that the rules are consistent with the OPE limit and that we recover the S-matrix optical theorem in the flat space limit. The AdS cutting rules and the CFT dispersion formula together form a holographic unitarity method to reconstruct Witten diagrams from their cuts.

scholarly journals Landau diagrams in AdS and S-matrices from conformal correlators

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Shota Komatsu ◽  
Miguel F. Paulos ◽  
Balt C. van Rees ◽  
Xiang Zhao
Keyword(s):  
Flat Space ◽  
Momentum Conservation ◽  
Quantum Field Theories ◽  
Triangle Diagram ◽  
S Matrix ◽  
Space Limit ◽  
Anomalous Threshold ◽  
Delta Functions ◽  
Shell Particles ◽  
Do So

Abstract 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 position-space procedure to do so. It features a direct map from boundary positions to (on-shell) momenta and thereby relates cross ratios to Mandelstam invariants. This recipe succeeds in several examples, includes the momentum-conserving delta functions, and can be shown to imply the two proposals in [1] based on Mellin space and on the OPE data. Interestingly the procedure does not always work: the Landau singularities of a Feynman diagram are shown to be part of larger regions, to be called ‘bad regions’, where the flat-space limit of the Witten diagram diverges. To capture these divergences we introduce the notion of Landau diagrams in AdS. As in flat space, these describe on-shell particles propagating over large distances in a complexified space, with a form of momentum conservation holding at each bulk vertex. As an application we recover the anomalous threshold of the four-point triangle diagram at the boundary of a bad region.

Massive fermion particle production in de Sitter universe: Ambient space approach

2014 ◽  
Vol 29 (10) ◽  
pp. 1450051 ◽  
Author(s):  
Sepideh Mirabi
Keyword(s):  
Particle Production ◽  
Particle Creation ◽  
Flat Space ◽  
Ambient Space ◽  
Quantum Field ◽  
De Sitter ◽  
Spin Particle ◽  
Massive Spin ◽  
De Sitter Universe ◽  
Space Approach

In this paper, we study the massive spin-½ particle creation in de Sitter (dS) space where the related fields are written in (4+1)-dimensional bulk or the so-called ambient space approach. This approach mimics the flat space quantum field theory (QFT) and the field operators are defined globally on dS space. The main purpose of this study is defining the |in〉 and |out〉 modes for the proposed quantum field which has been written in terms of the dS plane wave in the 4+1 dimensions. We compute, via the Bogoliubov coefficients, the rate of particle creation in dS universe.

scholarly journals CFT in AdS and boundary RG flows

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Simone Giombi ◽  
Himanshu Khanchandani
Keyword(s):  
Free Energy ◽  
Correlation Functions ◽  
Equations Of Motion ◽  
Flat Space ◽  
De Sitter ◽  
Conformal Field ◽  
Anomalous Dimensions ◽  
Epsilon Expansion ◽  
Boundary Operators ◽  
Renormalization Group Flows

Abstract Using the fact that flat space with a boundary is related by a Weyl transformation to anti-de Sitter (AdS) space, one may study observables in boundary conformal field theory (BCFT) by placing a CFT in AdS. In addition to correlation functions of local operators, a quantity of interest is the free energy of the CFT computed on the AdS space with hyperbolic ball metric, i.e. with a spherical boundary. It is natural to expect that the AdS free energy can be used to define a quantity that decreases under boundary renormalization group flows. We test this idea by discussing in detail the case of the large N critical O(N) model in general dimension d, as well as its perturbative descriptions in the epsilon-expansion. Using the AdS approach, we recover the various known boundary critical behaviors of the model, and we compute the free energy for each boundary fixed point, finding results which are consistent with the conjectured F-theorem in a continuous range of dimensions. Finally, we also use the AdS setup to compute correlation functions and extract some of the BCFT data. In particular, we show that using the bulk equations of motion, in conjunction with crossing symmetry, gives an efficient way to constrain bulk two-point functions and extract anomalous dimensions of boundary operators.

scholarly journals AdS bulk locality from sharp CFT bounds

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Simon Caron-Huot ◽  
Dalimil Mazáč ◽  
Leonardo Rastelli ◽  
David Simmons-Duffin
Keyword(s):  
Central Charge ◽  
Flat Space ◽  
Effective Field ◽  
Dispersion Relations ◽  
Sharp Form ◽  
Conformal Bootstrap ◽  
S Matrix ◽  
Higher Spin ◽  
Single Trace ◽  
Infrared Divergences

Abstract It is a long-standing conjecture that any CFT with a large central charge and a large gap ∆gap in the spectrum of higher-spin single-trace operators must be dual to a local effective field theory in AdS. We prove a sharp form of this conjecture by deriving numerical bounds on bulk Wilson coefficients in terms of ∆gap using the conformal bootstrap. Our bounds exhibit the scaling in ∆gap expected from dimensional analysis in the bulk. Our main tools are dispersive sum rules that provide a dictionary between CFT dispersion relations and S-matrix dispersion relations in appropriate limits. This dictionary allows us to apply recently-developed flat-space methods to construct positive CFT functionals. We show how AdS4 naturally resolves the infrared divergences present in 4D flat-space bounds. Our results imply the validity of twice-subtracted dispersion relations for any S-matrix arising from the flat-space limit of AdS/CFT.

scholarly journals Revisiting Coleman-de Luccia transitions in the AdS regime using holography

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Jewel K. Ghosh ◽  
Elias Kiritsis ◽  
Francesco Nitti ◽  
Lukas T. Witkowski
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Flat Space ◽  
Field Theories ◽  
Quantum Field ◽  
De Sitter ◽  
Thin Walled ◽  
Scalar Theories ◽  
Scalar Potentials

Abstract Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3.

scholarly journals Modular invariant holographic correlators for $$ \mathcal{N} $$ = 4 SYM with general gauge group

2021 ◽  
Vol 2021 (12) ◽  
Author(s):  
Luis F. Alday ◽  
Shai M. Chester ◽  
Tobias Hansen
Keyword(s):  
Gauge Group ◽  
Flat Space ◽  
Closed Form Expression ◽  
Tree Level ◽  
Modular Invariant ◽  
Higher Derivative ◽  
S Matrix ◽  
Space Limit ◽  
Type Iib String Theory ◽  
General Gauge

Abstract We study the stress tensor four-point function for $$ \mathcal{N} $$ N = 4 SYM with gauge group G = SU(N), SO(2N + 1), SO(2N) or USp(2N) at large N . When G = SU(N), the theory is dual to type IIB string theory on AdS5× S5 with complexified string coupling τs, while for the other cases it is dual to the orbifold theory on AdS5× S5/ℤ2. In all cases we use the analytic bootstrap and constraints from localization to compute 1-loop and higher derivative tree level corrections to the leading supergravity approximation of the correlator. We give perturbative evidence that the localization constraint in the large N and finite complexified coupling τ limit can be written for each G in terms of Eisenstein series that are modular invariant in terms of τs ∝ τ, which allows us to fix protected terms in the correlator in that limit. In all cases, we find that the flat space limit of the correlator precisely matches the type IIB S-matrix. We also find a closed form expression for the SU(N) 1-loop Mellin amplitude with supergravity vertices. Finally, we compare our analytic predictions at large N and finite τ to bounds from the numerical bootstrap in the large N regime, and find that they are not saturated for any G and any τ , which suggests that no physical theory saturates these bootstrap bounds.

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