# Lessons from the Ramond sector

### Submission summary

 As Contributors: Nathan Benjamin · Ying-Hsuan Lin Arxiv Link: https://arxiv.org/abs/2005.02394v1 (pdf) Date accepted: 2020-10-30 Date submitted: 2020-05-26 02:00 Submitted by: Benjamin, Nathan Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We revisit the consistency of torus partition functions in (1+1)$d$ fermionic conformal field theories, combining traditional ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities. Various lessons can be learned by simply examining the oft-ignored Ramond sector. For several extremal/kinky modular functions in the bootstrap literature, we can either rule out or identify the underlying theory. We also revisit the ${\cal N} = 1$ Maloney-Witten partition function by calculating the spectrum in the Ramond sector, and further extending it to include the modular sum of seed Ramond characters. Finally, we perform the full ${\cal N} = 1$ RNS modular bootstrap and obtain new universal results on the existence of relevant deformations preserving different amounts of supersymmetry.

Published as SciPost Phys. 9, 065 (2020)

### Submission & Refereeing History

#### Published as SciPost Phys. 9, 065 (2020)

Submission 2005.02394v1 on 26 May 2020

## Reports on this Submission

### Report 2 by Sungjay Lee on 2020-10-4 (Invited Report)

• Cite as: Sungjay Lee, Report on arXiv:2005.02394v1, delivered 2020-10-04, doi: 10.21468/SciPost.Report.2042

### Report

In the paper under review, the authors carefully studied the consistency conditions on the fermionic CFTs in two dimensions. They elaborated on various constraints via examining the Ramond partition function. The paper presents many new results including the lower bounds on the central charge and the number of spin-two primaries for a given number of spin-one conserved currents, which plays an important role in exploring the landscape of 2d fermionic CFTs. I would therefore recommend the paper for publication.

• validity: high
• significance: high
• originality: high
• clarity: high
• formatting: excellent
• grammar: excellent

### Anonymous Report 1 on 2020-7-31 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2005.02394v1, delivered 2020-07-31, doi: 10.21468/SciPost.Report.1873

### Report

The paper ''Lessons from the Ramond sector'' by Benjamin and Lin derives novel constraints on partition functions, in the spirit of the bootstrap program. The paper is clearly explained and concisely written, and the results are significant enough to warrant publication.

The only comment I have is that it may be good to explain what the Arf invariant is, especially in the context of the paper. However, this is not a significant point.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Author:  Nathan Benjamin  on 2020-08-07  [id 920]

(in reply to Report 1 on 2020-07-31)

We thank the referee for the report. We have uploaded a v2 on the arxiv explaining the Arf invariant in Footnote 2 (as well as correcting various typos). (see https://arxiv.org/pdf/2005.02394.pdf)