An official website of the United States government
A<sc>bstract</sc> We generalize Coulomb-branch-based gauged linear sigma model (GLSM)–computations of quantum cohomology rings of Fano spaces. Typically such computations have focused on GLSMs without superpotential, for which the low energy limit of the GLSM is a pure Coulomb branch, and quantum cohomology is determined by the critical locus of a twisted one-loop effective superpotential. We extend these results to cases for which the low energy limit of the GLSM includes both Coulomb and Higgs branches, where the latter is a Landau-Ginzburg orbifold. We describe the state spaces and products of corresponding operators in detail, comparing a geometric phase description, where the operator product ring is quantum cohomology, to the description in terms of Coulomb and Higgs branch states. As a concrete test of our methods, we compare to existing mathematics results for quantum cohomology rings of hypersurfaces in projective spaces.
more »
« less
This content will become publicly available on June 1, 2026
Schubert defects in Lagrangian Grassmannians
A<sc>bstract</sc> In this paper, we propose a construction of GLSM defects corresponding to Schubert cycles in Lagrangian Grassmannians, following recent work of Closset-Khlaif on Schubert cycles in ordinary Grassmannians. In the case of Lagrangian Grassmannians, there are superpotential terms in both the bulk GLSM as well as on the defect itself, enforcing isotropy constraints. We check our construction by comparing the locus on which the GLSM defect is supported to mathematical descriptions, checking dimensions, and perhaps most importantly, comparing defect indices to known and expected polynomial invariants of the Schubert cycles in quantum cohomology and quantum K theory.
more »
« less
- PAR ID:
- 10614796
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2025
- Issue:
- 6
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)A bstract In this paper we explore nonabelian gauged linear sigma models (GLSMs) for symplectic and orthogonal Grassmannians and flag manifolds, checking e.g. global symmetries, Witten indices, and Calabi-Yau conditions, following up a proposal in the math community. For symplectic Grassmannians, we check that Coulomb branch vacua of the GLSM are consistent with ordinary and equivariant quantum cohomology of the space.more » « less
-
Abstract We give a simple and uniform proof of a conjecture of Haines–Richarz characterizing the smooth locus of Schubert varieties in twisted affine Grassmannians. Our method is elementary and avoids any representation theoretic techniques, instead relying on a combinatorial analysis of tangent spaces of Schubert varieties.more » « less
-
A<sc>bstract</sc> We give a general construction relating Narain rational conformal field theories (RCFTs) and associated 3d Chern-Simons (CS) theories to quantum stabilizer codes. Starting from an abelian CS theory with a fusion group consisting ofneven-order factors, we map a boundary RCFT to ann-qubit quantum code. When the relevant ’t Hooft anomalies vanish, we can orbifold our RCFTs and describe this gauging at the level of the code. Along the way, we give CFT interpretations of the code subspace and the Hilbert space of qubits while mapping error operations to CFT defect fields.more » « less
-
Spatially-coupled (SC) codes is a class of convolutional LDPC codes that has been well investigated in classical coding theory thanks to their high performance and compatibility with low-latency decoders. We describe toric codes as quantum counterparts of classical two-dimensional spatially-coupled (2D-SC) codes, and introduce spatially-coupled quantum LDPC (SC-QLDPC) codes as a generalization. We use the convolutional structure to represent the parity check matrix of a 2D-SC code as a polynomial in two indeterminates, and derive an algebraic condition that is both necessary and sufficient for a 2D-SC code to be a stabilizer code. This algebraic framework facilitates the construction of new code families. While not the focus of this paper, we note that small memory facilitates physical connectivity of qubits, and it enables local encoding and low-latency windowed decoding. In this paper, we use the algebraic framework to optimize short cycles in the Tanner graph of 2D-SC hypergraph product (HGP) codes that arise from short cycles in either component code. While prior work focuses on QLDPC codes with rate less than 1/10, we construct 2D-SC HGP codes with small memories, higher rates (about 1/3), and superior thresholds.more » « less
