Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Liendo, Pedro; Meneghelli, Carlo

doi:10.1007/jhep01(2017)122

Cited by 123 publications

(186 citation statements)

References 67 publications

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“…We will now derive, along the same lines as [32,40,70] 13) are invariant and will be denoted by x 1 , x 2 , y. It is easy to convince oneself that these are the only invariants by noticing that all fermionic coordinates in this four-point function can be set to zero by a superconformal transformation.…”

Section: Superconformal Ward Identitiesmentioning

confidence: 99%

“…A basic requirement in any superconformal bootstrap analysis is the computation of the superconformal blocks relevant for the theory in question, although correlation functions of half-BPS operators in various dimensions have been studied [31][32][33], the case of N = 3 has not yet been considered, and calculating the necessary blocks will be one of the goals of this paper. For literature on superconformal blocks see [31][32][33][34][35][36][37][38][39][40].…”

Section: Jhep04(2017)032mentioning

confidence: 99%

“…We will follow closely [40,70], where a similar approach was used to study correlation functions in several superconformal setups.…”

Section: Superblocksmentioning

confidence: 99%

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Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories

Lemos

Liendo

Meneghelli

et al. 2017

J. High Energ. Phys.

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We initiate the bootstrap program for N = 3 superconformal field theories (SCFTs) in four dimensions. The problem is considered from two fronts: the protected subsector described by a 2d chiral algebra, and crossing symmetry for half-BPS operators whose superconformal primaries parametrize the Coulomb branch of N = 3 theories. With the goal of describing a protected subsector of a family of N = 3 SCFTs, we propose a new 2d chiral algebra with super Virasoro symmetry that depends on an arbitrary parameter, identified with the central charge of the theory. Turning to the crossing equations, we work out the superconformal block expansion and apply standard numerical bootstrap techniques in order to constrain the CFT data. We obtain bounds valid for any theory but also, thanks to input from the chiral algebra results, we are able to exclude solutions with N = 4 supersymmetry, allowing us to zoom in on a specific N = 3 SCFT.

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Section: Superconformal Ward Identitiesmentioning

confidence: 99%

Section: Jhep04(2017)032mentioning

confidence: 99%

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Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories

Lemos

Liendo

Meneghelli

et al. 2017

J. High Energ. Phys.

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“…The harmonics, P J (w) are obtained by inserting the quadratic Casimir for SU (2) R in the four-point function, in a similar way to what is usually done to obtain bosonic conformal blocks, 22) and are related to the R-symmetry projectors,…”

Section: R-symmetry Variablesmentioning

confidence: 99%

“…For such multiplets, the shortening conditions greatly simplify the structure of the conformal blocks. With eight Poincaré supercharges and an R-symmetry group containing SU (2) R , results are known for conformal blocks of four-point functions involving half-BPS operators in 3D, N = 4 [21,22], 4D, N = 2 [23,24], 5D, N = 1 [25] and 6D, N = (1, 0) [26,27].…”

Section: Introductionmentioning

confidence: 99%

Superconformal blocks for mixed 1/2-BPS correlators with SU(2) R-symmetry

Baume

Fuchs

Lawrie

2019

J. High Energ. Phys.

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For SCFTs with an SU (2) R-symmetry, we determine the superconformal blocks that contribute to the four-point correlation function of a priori distinct half-BPS superconformal primaries as an expansion in terms of the relevant bosonic conformal blocks. This is achieved by using the superconformal Casimir equation and the superconformal Ward identity to fix the coefficients of the bosonic blocks uniquely in a dimension-independent way. In addition we find that many of the resulting coefficients are related through a web of linear transformations of the conformal data. a very nice playground to study non-perturbative effects and relations to string theory, for instance their connection to the swampland program [38].As six is the largest dimension allowing for a superconformal algebra [39], N = (1, 0)representation theory provides an overarching language encompassing lower dimensions via dimensional reduction 3 . Let us review the possible multiplets allowed in theories with SU (2) R R-symmetry [19, 20]. There can exist states which are annihilated by a subset of the supercharges. These null states must be absent in unitary theories, and lead to what are referred as short multiplets, as opposed to long multiplets, which do not have null states. It is standard to write long multiplets as L[∆, , J R ], where ∆ is the conformal dimension of the superconformal primary, denotes how the superconformal primary transforms as a traceless-symmetric 4 representation of so(1, d − 1) rotations of the Poincaré algebra, and J R is the charge under SU (2) R . The different short multiplets are denoted as the A-, B-, C-, and D-type multiplets. Unitarity gives lower bounds on the allowed conformal dimensions, ∆, of the superconformal primaries of long multiplets, and is moreover strong enough to completely fix the conformal dimension of the short multiplets as a function of the other group theoretical data and the spacetime dimension. The superconformal multiplets can be summarised as follows : L[∆, , J R ] : ∆ > 2ε J R + + µ , A[ , J R ] : ∆ = 2ε J R + + 4ε − 2 , B[ , J R ] : ∆ = 2ε J R + + 2ε , (1.1) C[J R ] : ∆ = 2ε J R + 2 , D[J R ] : ∆ = 2ε J R ,with ε = (d − 2)/2, µ = 2ε for 2 < d ≤ 4 and µ = 4ε − 2 for 4 ≤ d ≤ 6. We stress again that this corresponds to the standard notation for d = 6. Indeed, A-type multiplets correspond to the unitarity bound of long multiplets, which for d ≤ 4 coincides with the bound of type B. Type C is unique to six dimensions and can be traced back to the presence of self-dual two-forms. Moreover, type C and D will appear only with = 0, since in this work we 3 We note that for d ≤ 4, the nomenclature we are using here might not match the one the reader is familiar with. For instance, in four dimensions, the classification of half-BPS multiplets is refined into Higgs and Coulomb type, commonly denoted E r andB R respectively [40]. We refer to [20] for a dictionary between the 6D notation and lower dimensions.4 In this paper we will consider only multiplets that have a superconformal primary in a traceles...

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Defects in Conformal Field Theories

Lauria¹

2019

Springer Theses

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Bootstrap equations for N $$ \mathcal{N} $$ = 4 SYM with defects

Cited by 123 publications

References 67 publications

Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories

Bootstrapping N = 3 $$ \mathcal{N}=3 $$ superconformal theories

Superconformal blocks for mixed 1/2-BPS correlators with SU(2) R-symmetry

Defects in Conformal Field Theories

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