TY - JOUR

T1 - Towards general super Casimir equations for 4D N= 1 SCFTs

AU - Ramírez, Israel A.

N1 - Funding Information:
Article funded by SCOAP3.
Funding Information:
I would like to thank P. Liendo and M. Lemos for collaborations at early stages of this work. I would also like to thank Nikolay Bobev, Edoardo Lauria, Per Sundell and Gerben Venken for useful comments and inspiring discussions. I would especially like to thank S. Retamales, for her comments, suggestions and much more. Finally, I would like to thanks Helena Ramírez for pointing out the missing C1 term in (3.31) and (3.39). I.A.R. is supported by FONDECYT grant No. 3170373.

PY - 2019/3/1

Y1 - 2019/3/1

N2 -
Applying the Casimir operator to four-point functions in CFTs allows us to find the conformal blocks for any external operators. In this work, we initiate the program to find the superconformal blocks, using the super Casimir operator, for 4DN= 1 SCFTs. We begin by finding the most general four-point function with zero U(1)
R
-charge, including all the possible nilpotent structures allowed by the superconformal algebra. We then study particular cases where some of the operators satisfy shortening conditions. Finally, we obtain the super Casimir equations for four point-functions which contain a chiral and an anti-chiral field. We solve the super Casimir equations by writing the superconformal blocks as a sum of several conformal blocks.

AB -
Applying the Casimir operator to four-point functions in CFTs allows us to find the conformal blocks for any external operators. In this work, we initiate the program to find the superconformal blocks, using the super Casimir operator, for 4DN= 1 SCFTs. We begin by finding the most general four-point function with zero U(1)
R
-charge, including all the possible nilpotent structures allowed by the superconformal algebra. We then study particular cases where some of the operators satisfy shortening conditions. Finally, we obtain the super Casimir equations for four point-functions which contain a chiral and an anti-chiral field. We solve the super Casimir equations by writing the superconformal blocks as a sum of several conformal blocks.

KW - Conformal and W Symmetry

KW - Conformal Field Theory

KW - Superspaces

KW - Supersymmetry and Duality

UR - http://www.scopus.com/inward/record.url?scp=85062608538&partnerID=8YFLogxK

U2 - 10.1007/JHEP03(2019)047

DO - 10.1007/JHEP03(2019)047

M3 - Article

AN - SCOPUS:85062608538

VL - 2019

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 3

M1 - 47

ER -