Boundaries, Vermas and factorisation

We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $$ \mathcal{N} $$ N ≥ 4 supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

“…9. A derivation of the IR formula using holomorphic factorisation was provided in[70]. We thank the authors for bringing this work to our attention.…”

mentioning

confidence: 99%

Localization and duality for ABJM latitude Wilson loops

Guerrini

Yaakov

2021

“…found in [25]. Examples of N = (0, 2) boundaries and interfaces can be found in [69][70][71][72][73][74][75][76][77][78]. We will follow the conventions of [77] here.…”

Section: Boundaries In 3d Scftsmentioning

confidence: 99%

Surface defect, anomalies and b-extremization

Wang

2021

Quantum field theories (QFT) in the presence of defects exhibit new types of anomalies which play an important role in constraining the defect dynamics and defect renormalization group (RG) flows. Here we study surface defects and their anomalies in conformal field theories (CFT) of general spacetime dimensions. When the defect is conformal, it is characterized by a conformal b-anomaly analogous to the c-anomaly of 2d CFTs. The b-theorem states that b must monotonically decrease under defect RG flows and was proven by coupling to a spurious defect dilaton. We revisit the proof by deriving explicitly the dilaton effective action for defect RG flow in the free scalar theory. For conformal surface defects preserving $$ \mathcal{N} $$ N = (0, 2) supersymmetry, we prove a universal relation between the b-anomaly and the ’t Hooft anomaly for the U(1)r symmetry. We also establish the b-extremization principle that identifies the superconformal U(1)r symmetry from $$ \mathcal{N} $$ N = (0, 2) preserving RG flows. Together they provide a powerful tool to extract the b-anomaly of strongly coupled surface defects. To illustrate our method, we determine the b-anomalies for a number of surface defects in 3d, 4d and 6d SCFTs. We also comment on manifestations of these defect conformal and ’t Hooft anomalies in defect correlation functions.

“…With the systematic study of rigid supersymmetry on curved manifolds [15,16], all possible manifolds on which at least N = 2 supersymmetry can be preserved have been classified and corresponding partition functions Z M 3 have been computed, with the possible exception of the 3-torus T 3 [17][18][19][20]. Among them is the partition function on a manifold given by the twisted product of a disk (2d hemisphere) and a circle: D 2 × q S 1 [21][22][23], where q is a deformation parameter of D 2 . This partition function is also known as a holomorphic block.…”

Section: Introductionmentioning

confidence: 99%

Stokes phenomena in 3d $$ \mathcal{N} $$ = 2 SQED2 and $$ \mathbbm{CP} $$1 models

Jain

Manna

2021

We propose a novel approach of uncovering Stokes phenomenon exhibited by the holomorphic blocks of $$ \mathbbm{CP} $$ CP 1 model by considering it as a specific decoupling limit of SQED2 model. This approach involves using a ℤ3 symmetry that leaves the supersymmetric parameter space of SQED2 model invariant to transform a pair of SQED2 holomorphic blocks to get two new pairs of blocks. The original pair obtained by solving the line operator identities of the SQED2 model and the two new transformed pairs turn out to be related by Stokes-like matrices. These three pairs of holomorphic blocks can be reduced to the known triplet of $$ \mathbbm{CP} $$ CP 1 blocks in a particular decoupling limit where two of the chiral multiplets in the SQED2 model are made infinitely massive. This reduction then correctly reproduces the Stokes regions and matrices of the $$ \mathbbm{CP} $$ CP 1 blocks. Along the way, we find six pairs of SQED2 holomorphic blocks in total, which lead to six Stokes-like regions covering uniquely the full parameter space of the SQED2 model.