D-brane central charge and Landau-Ginzburg orbifolds
type: Item
instance of: scholarly article
title: D-brane central charge and Landau-Ginzburg orbifolds
zbMATH Open document ID: 1469.81060
author: Johanna Knapp
author: Mauricio Romo
author: Emanuel Scheidegger
published in: Communications in Mathematical Physics
publication date: 2021-05-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/2003.00182
review text: The current paper under review discusses the central charge of a B-type D-brane \(\mathcal{B}\) in the context of \(\mathcal{N}=(2,2)\) superconformal field theories (SCFT). The paper suggests a universal expression \(Z_{\text{SCFT}}(\mathcal{B})= \langle \widehat{\Gamma}^* \circ \mathbf{J} \mid \text{ch}(\mathcal{B})\rangle\) for the central charge and provides a convincing evidence for why this is the right definition in some crucial case. To explain the context of the evidence, note an important fact that non-anomalous (aka Calabi-Yau) gauged linear sigma models (GLSM) flow to those SCFTs in the low-energy limit under the renormalization group flow. On the other hand, it is known by Hori and Romo's earlier work (``Exact results in two-dimensional (2,2) supersymmetric gauge theories with boundary'') that the central charge of a B-brane \(\widetilde{\mathcal{B}}\) of GLSM can be understood as the hemisphere partition function \(Z_{D^2}(\widetilde{\mathcal{B}})\). This suggests that if a GLSM flows to a SCFT such that \(\widetilde{\mathcal B}\) corresponds to \(\mathcal B\), then their central charges \(Z_{D^2}(\widetilde{\mathcal{B}})\) and \(Z_{\text{SCFT}}(\mathcal{B})\) should coincide. This was known previously for a geometric phase. The current paper argues for an LG orbifold phase. Let us be more concrete. For the input data of GLSM, one considers a quadruple \((G,\rho_V, W,R)\), where \(G\) is a compact Lie group (gauge group), \(\rho_V\colon G\to GL(V)\cong GL(\mathbb{C}^N)\) a faithful finite-dimensional representation (chiral matter fields), \(W\in \text{Sym}(V^*)^G\) (superpotential), and \( R\colon U(1)_V\to GL(V)\), say \(\lambda \cdot (z_1,\cdots,z_N) = (\lambda^{q_1}z_1,\cdots,\lambda^{q_n}z_n )\) (vector R-charge). A GLSM being non-anomalous means that \(\rho_V \) factors through \(SL(V)\), i.e., the axial R-charge \(U(1)_A\) is non-anomalous. We also ask that \(W\) satisfies \(W( \lambda \cdot z ) = \lambda^2 W(z)\), i.e., the superpotential preser…
reviewed by: Philsang Yoo
Mathematics Subject Classification ID: 81T40
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 32Q25
Mathematics Subject Classification ID: 14D21
Mathematics Subject Classification ID: 81T13
zbMATH DE Number: 7348147
zbMATH Keywords: Landau-Ginzburg orbifold
zbMATH Keywords: central charge formula
describes a project that uses: PALP
MaRDI profile type: Publication
OpenAlex ID: W3007126343
arXiv ID: 2003.00182
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D-brane central charge and Landau-Ginzburg orbifolds (DOI)
DOI: 10.1007/S00220-021-04042-W