scholarly journals Large N correlation functions in superconformal field theories

2016 ◽  
Vol 2016 (6) ◽  
Author(s):  
Diego Rodriguez-Gomez ◽  
Jorge G. Russo
Keyword(s):  
Correlation Functions ◽  
Field Theories ◽  
Superconformal Field Theories ◽  
Large N

scholarly journals Correlation functions of spinor current multiplets in $$ \mathcal{N} $$ = 1 superconformal theory

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Evgeny I. Buchbinder ◽  
Jessica Hutomo ◽  
Sergei M. Kuzenko
Keyword(s):  
Field Theory ◽  
Correlation Functions ◽  
Field Theories ◽  
Point Function ◽  
Superconformal Field Theories ◽  
Superconformal Symmetry ◽  
Four Dimensions ◽  
Superconformal Field Theory ◽  
Superconformal Theories ◽  
Spinor Current

Abstract We consider $$ \mathcal{N} $$ N = 1 superconformal field theories in four dimensions possessing an additional conserved spinor current multiplet Sα and study three-point functions involving such an operator. A conserved spinor current multiplet naturally exists in superconformal theories with $$ \mathcal{N} $$ N = 2 supersymmetry and contains the current of the second supersymmetry. However, we do not assume $$ \mathcal{N} $$ N = 2 supersymmetry. We show that the three-point function of two spinor current multiplets and the $$ \mathcal{N} $$ N = 1 supercurrent depends on three independent tensor structures and, in general, is not contained in the three-point function of the $$ \mathcal{N} $$ N = 2 supercurrent. It then follows, based on symmetry considerations only, that the existence of one more Grassmann odd current multiplet in $$ \mathcal{N} $$ N = 1 superconformal field theory does not necessarily imply $$ \mathcal{N} $$ N = 2 superconformal symmetry.

scholarly journals Five-dimensional non-Lorentzian conformal field theories and their relation to six-dimensions

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
N. Lambert ◽  
A. Lipstein ◽  
R. Mouland ◽  
P. Richmond
Keyword(s):  
Correlation Functions ◽  
Conformal Symmetry ◽  
Field Theories ◽  
Conformal Field Theories ◽  
Dimensional Theory ◽  
Superconformal Field Theories ◽  
Yang Mills ◽  
Conformal Field ◽  
Instanton Number ◽  
Do So

Abstract We study correlation functions in five-dimensional non-Lorentzian theories with an SU(1, 3) conformal symmetry. Examples of such theories have recently been obtained as Ω-deformed Yang-Mills Lagrangians arising from a null reduction of six-dimensional superconformal field theories on a conformally compactified Minkowski space. The correlators exhibit a rich structure with many novel properties compared to conventional correlators in Lorentzian conformal field theories. Moreover, identifying the instanton number with the Fourier mode number of the dimensional reduction offers a hope to formulate six-dimensional conformal field theories in terms of five-dimensional Lagrangian theories. To this end we show that the Fourier decompositions of six-dimensional correlation functions solve the Ward identities of the SU(1, 3) symmetry, although more general solutions are possible. Conversely we illustrate how one can reconstruct six-dimensional correlation functions from those of a five-dimensional theory, and do so explicitly at 2- and 3-points. We also show that, in a suitable decompactification limit Ω → 0, the correlation functions become those of the DLCQ description.

scholarly journals ON INVARIANTS AND SCALAR CHIRAL CORRELATION FUNCTIONS IN ${\mathcal N} = 1$ SUPERCONFORMAL FIELD THEORIES

2011 ◽  
Vol 26 (12) ◽  
pp. 2007-2025
Author(s):  
HOLGER KNUTH
Keyword(s):  
Differential Operator ◽  
Arbitrary Function ◽  
Correlation Functions ◽  
Field Theories ◽  
Point Function ◽  
Superconformal Field Theories ◽  
Linearly Independent ◽  
General Scalar ◽  
Superconformal Theories ◽  
Chiral Superfields

A general expression for the four-point function with vanishing total R-charge of antichiral and chiral superfields in [Formula: see text] superconformal theories is given. It is obtained by applying the exponential of a simple universal nilpotent differential operator to an arbitrary function of two cross-ratios. To achieve this the nilpotent superconformal invariants according to Park are focused. Several dependencies between these invariants are presented, so that eight nilpotent invariants and 27 monomials of these invariants of degree d > 1 are left being linearly independent. It is analyzed, how terms within the four-point function of general scalar superfields cancel in order to fulfill the chiral restrictions.

Modular invariance in N=2 superconformal field theories

1987 ◽  
Vol 195 (2) ◽  
pp. 202-208 ◽  
Author(s):  
Francesco Ravanini ◽  
Sung-Kil Yang
Keyword(s):  
Field Theories ◽  
Modular Invariance ◽  
Superconformal Field Theories

scholarly journals 5d and 4d SCFTs: canonical singularities, trinions and S-dualities

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Cyril Closset ◽  
Simone Giacomelli ◽  
Sakura Schäfer-Nameki ◽  
Yi-Nan Wang
Keyword(s):  
String Theory ◽  
Field Theories ◽  
Flavor Symmetry ◽  
Crepant Resolution ◽  
Superconformal Field Theories ◽  
Hypersurface Singularities ◽  
Canonical Singularities ◽  
Type Iib String Theory ◽  
M Theory

Abstract Canonical threefold singularities in M-theory and Type IIB string theory give rise to superconformal field theories (SCFTs) in 5d and 4d, respectively. In this paper, we study canonical hypersurface singularities whose resolutions contain residual terminal singularities and/or 3-cycles. We focus on a certain class of ‘trinion’ singularities which exhibit these properties. In Type IIB, they give rise to 4d $$ \mathcal{N} $$ N = 2 SCFTs that we call $$ {D}_p^b $$ D p b (G)-trinions, which are marginal gaugings of three SCFTs with G flavor symmetry. In order to understand the 5d physics of these trinion singularities in M-theory, we reduce these 4d and 5d SCFTs to 3d $$ \mathcal{N} $$ N = 4 theories, thus determining the electric and magnetic quivers (or, more generally, quiverines). In M-theory, residual terminal singularities give rise to free sectors of massless hypermultiplets, which often are discretely gauged. These free sectors appear as ‘ugly’ components of the magnetic quiver of the 5d SCFT. The 3-cycles in the crepant resolution also give rise to free hypermultiplets, but their physics is more subtle, and their presence renders the magnetic quiver ‘bad’. We propose a way to redeem the badness of these quivers using a class $$ \mathcal{S} $$ S realization. We also discover new S-dualities between different $$ {D}_p^b $$ D p b (G)-trinions. For instance, a certain E8 gauging of the E8 Minahan-Nemeschansky theory is S-dual to an E8-shaped Lagrangian quiver SCFT.

scholarly journals Complete prepotential for 5d $$ \mathcal{N} $$ = 1 superconformal field theories

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Hirotaka Hayashi ◽  
Sung-Soo Kim ◽  
Kimyeong Lee ◽  
Futoshi Yagi
Keyword(s):  
Field Theories ◽  
Superconformal Field Theories
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