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B-type D-branes in hybrid models

by Johanna Knapp, Robert Pryor

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Submission summary

Authors (as registered SciPost users): Robert Pryor
Submission information
Preprint Link: https://arxiv.org/abs/2404.14613v2  (pdf)
Date accepted: Nov. 12, 2024
Date submitted: June 26, 2024, 9:21 a.m.
Submitted by: Robert Pryor
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
Specialties:
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

A hybrid model is a fibration of a Landau-Ginzburg orbifold over a geometric base. We study B-type D-branes in hybrid models. Imposing B-type supersymmetry on the boundary action, we show that D-branes are specified by matrix factorisations in the fibre direction, together with some geometric data associated to the base. We also deduce conditions for the compatibility of these branes with the bulk orbifold actions and R-symmetry. We construct examples of hybrid B-branes which are generalisations of well-studied branes in geometric and Landau-Ginzburg models. Hybrid models can arise at limiting points of the stringy Kahler moduli space of Calabi-Yaus, and can be realised as phases of the corresponding gauged linear sigma models (GLSMs). Using GLSM techniques, we establish connections between geometric branes and hybrid branes. As explicit examples, we consider one- and two-parameter Calabi-Yau hybrids with a $\mathbb{P}^1$-base.

Author indications on fulfilling journal expectations

  • Provide a novel and synergetic link between different research areas.
  • Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
  • Detail a groundbreaking theoretical/experimental/computational discovery
  • Present a breakthrough on a previously-identified and long-standing research stumbling block

Published as SciPost Phys. 17, 165 (2024)

Reports on this Submission

Report #4 by Anonymous (Referee 2) on 2024-10-31 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2404.14613v2, delivered 2024-10-31, doi: 10.21468/SciPost.Report.10014

Strengths

This is a well-written paper, which discusses matrix factorizations in hybrid Landau-Ginzburg models. Examples of such matrix factorizations have been discussed elsewhere, but this is the first detailed, general, first-principles account of which I'm aware. It explicitly discussses their construction as a set of ordinary matrix factorizations in Landau-Ginzburg models in sections of the hybrid, together with overlap data, and also gives detailed computations.

Weaknesses

A minor point is that this is a rather technical area, of interest primarily to experts. Another minor point is that it might be nice to have a few more examples, but, the paper is already rather long.

Report

Briefly, I recommend this paper for publication. It meets the journal's standards.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

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

Report #3 by Anonymous (Referee 1) on 2024-10-27 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2404.14613v2, delivered 2024-10-27, doi: 10.21468/SciPost.Report.9987

Strengths

Generally the paper is of good quality. The authors carefully develop the subject in a well readable manner, and spice it up with a variety of detailed computations for examples. These are at the core of the paper, and help the moderately informed physicist to grasp the considerable mathematical complexity of the subject. Upon cursory inspection the computations appear to be correct (there is a minor typo in the second-to-last paragraph of Sect. 6.)

Weaknesses

The subject of hybrid branes is quite specialised but definitely of interest to people working in the field.

Report

The authors extend the framework of matrix factorisations, which describe topological B-branes in N=(2,2) superconformal field theories, to so-called hybrid branes. "Hybrid" denotes here the general phase of two-dimensional
N=(2,2) superconformal field theories, which can be thought of as a mixture between the geometrical sigma-model phase and the Landau-Ginzburg phase; concretely this can be described as a sigma-model with additional superpotential. Correspondingly, also at the boundary where the D-branes live, general D-branes can be hybrid mixtures displaying both geometric and algebraic components; the latter being described in terms of matrix factorisations which in a concrete sense are fibered over the geometry. The total hybrid object is described as a "global matrix factorisation".

Given that hybrid phases of two dimensional N=(2,2) superconformal field theories are the most generic ones, it is evidently important to extend this structure to D-branes at the boundary. It is somewhat surprising that the issue wasn't addressed in depth before, and in retrospective the present work was overdue.

Recommendation

Publish (easily meets expectations and criteria for this Journal; among top 50%)

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

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