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Corrections of an elliptic block in the NS sector

Kangning Liu

Abstract

We propose a correction to one of the elliptic blocks in the NS sector of 2d $\mathcal N = 1$ superconformal field theories. We analyze the 4-point block in the pillow geometry to demonstrate the necessity of the correction and verify the formula by numerically checking the crossing symmetries in the $\mathcal N =1 $ super Liouville theory, as well as directly comparing the $c$-recursion and $h$-recursion results.

Corrections of an elliptic block in the NS sector

Abstract

We propose a correction to one of the elliptic blocks in the NS sector of 2d superconformal field theories. We analyze the 4-point block in the pillow geometry to demonstrate the necessity of the correction and verify the formula by numerically checking the crossing symmetries in the super Liouville theory, as well as directly comparing the -recursion and -recursion results.
Paper Structure (10 sections, 60 equations, 1 figure)

This paper contains 10 sections, 60 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Conformal blocks in NS sector of $\mathcal{N} = 1$ SCFT
  3. $c$-recursion
  4. $h$-recursion
  5. Determination of the correction
  6. Numerical checks
  7. Pillow correlation function
  8. Crossing symmetry
  9. Direct checks
  10. Conclusion

Figures (1)

  • Figure 1: Crossing symmetry of $\left\langle V_{P_1}(0) W_{P_2}(z,\bar{z})W_{P_3}(1)V_{P_4}(\infty)\right\rangle_{g=0}$