A
bstract
We revisit the problem of performing conformal block decomposition of exchange Witten diagrams in the crossed channel. Using properties of conformal blocks and Witten diagrams, we discover ...infinitely many linear relations among the crossed channel decomposition coefficients. These relations allow us to formulate a recursive algorithm that solves the decomposition coefficients in terms of certain seed coefficients. In one dimensional CFTs, the seed coefficient is the decomposition coefficient of the double-trace operator with the lowest conformal dimension. In higher dimensions, the seed coefficients are the coefficients of the double-trace operators with the minimal conformal twist. We also discuss the conformal block decomposition of a generic contact Witten diagram with any number of derivatives. As a byproduct of our analysis, we obtain a similar recursive algorithm for decomposing conformal partial waves in the crossed channel.
A
bstract
We present a universal treatment for imposing superconformal constraints on Mellin amplitudes for SCFT
d
with 3 ≤
d
≤ 6. This leads to a new technique to compute holographic correlators, ...which is similar but complementary to the ones introduced in
1
,
2
. We apply this technique to theories in various spacetime dimensions. In addition to reproducing known results, we obtain a simple expression for next-next-to-extremal four-point functions in
AdS
7
×
S
4
. We also use this machinery on
AdS
4
×
S
7
and compute the first holographic one-half BPS four-point function. We extract the anomalous dimension of the R-symmetry singlet double-trace operator with the lowest conformal dimension and find agreement with the 3d
N
=
8
numerical bootstrap bound at large central charge.
A
bstract
Witten diagrams are basic objects for studying dynamics in AdS space, and also play key roles in the analytic functional bootstrap. However, these diagrams are notoriously hard to evaluate, ...making it extremely difficult to search for recursion relations among them. In this note, we present simple methods to obtain recursion relations for exchange Witten diagrams from conformal block recursion relations. We discover a variety of new relations, including the dimensional reduction formulae for exchange Witten diagrams. In particular, we find a five-term recursion relation relating exchange Witten diagrams in
d
and
d −
2 dimensions. This gives the holographic analogue of a similar formula for conformal blocks due to Parisi-Sourlas supersymmetry. We also extend the analysis to two-point functions in CFTs with conformal boundaries, and obtain similar results.
A
bstract
We extend the Mellin space techniques of 1 for computing holographic four-point correlation functions in maximally superconformal theories to theories with only eight Poincaré supercharges. ...The one-half BPS operators in these correlators are taken to be the superconformal primary in the
D
k
multiplet (with
k
= 2 corresponding to the flavor current multiplet), and transform in the adjoint representation of a flavor group
G
. Because of the smaller R-symmetry group SU(2), each individual superconformal Ward identity is less powerful. On the other hand, the constraining power is compensated in number by the different flavor channels in the four-point function. As concrete test cases, we study the Seiberg theories in five dimensions and E-string theory in six dimensions at the large
N
limit. We show that the flavor current multiplet four-point functions are fixed by superconformal symmetry up to two free parameters, which are proportional to the squared OPE coefficients for the flavor current multiplet and the stress tensor multiplet.
A
bstract
We give a detailed account of the methods introduced in
1
to calculate holographic four-point correlators in IIB supergravity on AdS
5
×
S
5
. Our approach relies entirely on general ...consistency conditions and maximal supersymmetry. We discuss two related methods, one in position space and the other in Mellin space. The position space method is based on the observation that the holographic four-point correlators of one-half BPS single-trace operators can be written as finite sums of contact Witten diagrams. We demonstrate in several examples that imposing the superconformal Ward identity is sufficient to fix the parameters of this ansatz uniquely, avoiding the need for a detailed knowledge of the supergravity effective action. The Mellin space approach is an “on-shell method” inspired by the close analogy between holographic correlators and flat space scattering amplitudes. We conjecture a compact formula for the four-point correlators of one-half BPS single-trace operators of arbitrary weights. Our general formula has the expected analytic structure, obeys the superconformal Ward identity, satisfies the appropriate asymptotic conditions and reproduces all the previously calculated cases. We believe that these conditions determine it uniquely.
A
bstract
We demonstrate the simplicity of
AdS
5
× S
5
IIB supergravity at one loop level, by studying non-planar holographic four-point correlators in Mellin space. We develop a systematic algorithm ...for constructing one-loop Mellin amplitudes from the tree-level data, and obtain a simple closed form answer for the
O
2
SG
O
2
SG
O
p
SG
O
p
SG
correlators. The structure of this expression is remarkably simple, containing only simultaneous poles in the Mellin variables. We also study the flat space limit of the Mellin amplitudes, which reproduces precisely the IIB supergravity one-loop amplitude in ten dimensions. Our results provide nontrivial evidence for the persistence of the hidden conformal symmetry at one loop.
Gluon scattering in AdS from CFT Alday, Luis F.; Behan, Connor; Ferrero, Pietro ...
The journal of high energy physics,
06/2021, Letnik:
2021, Številka:
6
Journal Article
Recenzirano
Odprti dostop
A
bstract
We present a systematic study of holographic correlators in a vast array of SCFTs with non-maximal superconformal symmetry. These theories include 4d
N
= 2 SCFTs from D3-branes near ...F-theory singularities, 5d Seiberg exceptional theories and 6d E-string theory, as well as 3d and 4d phenomenological models with probe flavor branes. We consider current multiplets and their generalizations with higher weights, dual to massless and massive super gluons in the bulk. At leading order in the inverse central charge expansion, connected four-point functions of these operators correspond to tree-level gluon scattering amplitudes in AdS. We show that all such tree-level four-point amplitudes in all these theories are fully fixed by symmetries and consistency conditions and explicitly construct them. Our results encode a wealth of SCFT data and exhibit various interesting emergent structures. These include Parisi-Sourlas-like dimensional reductions, hidden conformal symmetry and an AdS version of the color-kinematic duality.
A
bstract
We develop an analytic approach to the four-point crossing equation in CFT, for general spacetime dimension. In a unitary CFT, the crossing equation (for, say, the
s
- and
t
-channel ...expansions) can be thought of as a vector equation in an infinite-dimensional space of complex analytic functions in two variables, which satisfy a boundedness condition at infinity. We identify a useful basis for this space of functions, consisting of the set of s-
and
t-channel conformal blocks of double-twist operators in mean field theory. We describe two independent algorithms to construct the
dual
basis of linear functionals, and work out explicitly many examples. Our basis of functionals appears to be closely related to the CFT dispersion relation recently derived by Carmi and Caron-Huot.
A
bstract
We revisit the calculation of holographic correlators for eleven-dimensional supergravity on
AdS
7
×
S
4
. Our methods rely entirely on symmetry and eschew detailed knowledge of the ...supergravity effective action. By an extension of the position space approach developed in 1, 2 for the
AdS
5
×
S
5
background, we compute four-point correlators of one-half BPS operators for identical weights
k
= 2
,
3
,
4. The
k
= 2 case corresponds to the four-point function of the stress-tensor multiplet, which was already known, while the other two cases are new. We also translate the problem in Mellin space, where the solution of the superconformal Ward identity takes a surprisingly simple form. We formulate an algebraic problem, whose (conjecturally unique) solution corresponds to the general one-half BPS four-point function.
An analytic approach to BCFTd Mazáč, Dalimil; Rastelli, Leonardo; Zhou, Xinan
The journal of high energy physics,
12/2019, Letnik:
2019, Številka:
12
Journal Article
Recenzirano
Odprti dostop
A
bstract
We develop an analytic approach to Boundary Conformal Field Theory (BCFT), focussing on the two-point function of a general pair of scalar primary operators. The resulting crossing equation ...can be thought of as a vector equation in an infinite-dimensional space
V
of analytic functions of a single complex variable. We argue that in a unitary theory, functions in
V
satisfy a boundedness condition in the Regge limit. We identify a useful basis for
V
, consisting of bulk
and
boundary conformal blocks with scaling dimensions which appear in OPEs of the mean field theory correlator. Our main achievement is an explicit expression for the action of the
dual
basis (the basis of linear functionals on
V
) on an arbitrary conformal block. The practical merit of our basis is that it trivializes the study of perturbations around mean field theory. Our results are equivalent to a BCFT version of the Polyakov bootstrap. Our derivation of the expressions for the functionals relies on the identification of the Polyakov blocks with (suitably improved) boundary and bulk Witten exchange diagrams in AdS
d
+1
. We also provide another conceptual perspective on the Polyakov block expansion and the associated functionals, by deriving a new Lorentzian OPE inversion formula for BCFT.
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