# Entanglement Negativity in Flat Holography

### Submission summary

 As Contributors: Debarshi Basu · Himanshu Parihar · Gautam Sengupta Preprint link: scipost_202107_00037v1 Date submitted: 2021-07-21 08:45 Submitted by: Sengupta, Gautam Submitted to: SciPost Physics Academic field: Physics Specialties: High-Energy Physics - Theory Approach: Theoretical

### Abstract

We advance holographic constructions for the entanglement negativity of bipartite states in a class of $(1+1)-$dimensional Galilean conformal field theories dual to asymptotically flat three dimensional bulk geometries described by Einstein Gravity and Topologically Massive Gravity. The construction involves specific algebraic sums of the lengths of bulk extremal curves homologous to certain combinations of the intervals appropriate to such bipartite states. Our analysis exactly reproduces the corresponding replica technique results in the large central charge limit. We substantiate our construction through a semi classical analysis involving the geometric monodromy technique for the case of two disjoint intervals in such holographic Galilean conformal field theories.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission scipost_202107_00037v1 on 21 July 2021

## Reports on this Submission

### Strengths

The authors consider various cases and perform several checks of their results.

### Weaknesses

Unclear what new physics the results obtained teach us.

### Report

A potentially interesting result of this article is the large central charge negativity of two disjoint intervals. To compute it, the authors use the standard CFT monodromy method applied to the case of Galilean conformal symmetry with the help of [67].

They provide formula (104) for the Galilean conformal block associated with certain four point functions (relevant in the computation eg of entanglement, negativity etc). The result is valid in the large central charge limit, and when the dominant contribution comes from a light operator (and the monodromy is computed around a light operator).

In section 6.1.3, the authors apply (104) for computing the entanglement negativity of disjoint intervals. However, they simultaneously claim that the dominant contribution in this case comes from an operator that remains heavy in the large rental charge limit - like in [25]. I would be grateful if the authors could further clarify this point, before considering the article for publication.

### Requested changes

See above.

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

### Report

This paper studied extensively the holography negativity in flat holography, ranging form single interval to multiple intervals, from Einstein gravity to TMG. The paper is rather long and contains lots of small technical details. Without going through all the details, I find that the strategies and results look reasonable to me. Therefore, I would recommend the publication of the paper.

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