REVIEW 8 cited by
On S-Duality in Abelian Gauge Theory
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
U(1) gauge theory on ${\bf R}^4$ is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of $SL(2,{\bf Z})$. In this paper, the duality is studied on a general four-manifold and it is shown that the partition function is not a modular-invariant function but transforms as a modular form. This result plays an essential role in determining a new low-energy interaction that arises when N=2 supersymmetric Yang-Mills theory is formulated on a four-manifold; the determination of this interaction gives a new test of the solution of the model and would enter in computations of the Donaldson invariants of four-manifolds with $b_2^+\leq 1$. Certain other aspects of abelian duality, relevant to matters such as the dependence of Donaldson invariants on the second Stieffel-Whitney class, are also analyzed.
Forward citations
Cited by 8 Pith papers
-
$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation
Lattice Villain Maxwell theory realizes the theta subgroup of SL(2,Z) via Hamiltonian operators S and T2, with charge exchange, the Witten effect, and a non-invertible defect with Tambara-Yamagami fusion.
-
Non-relativistic limits of $\mathcal N=4$ supersymmetric Yang-Mills theory and S-duality
Constructs a family of non-relativistic limits of 4d MSYM via brane setups that organize into a 3D moduli space with nontrivial topology where PSL(2,Z) dualities act more complexly than in the relativistic theory, est...
-
Heisenberg-Euler and the Quantum Dilogarithm
Heisenberg-Euler effective Lagrangian is recast as a dispersion integral with the quantum dilogarithm as kernel, its imaginary part given directly by the dilogarithm and its real part involving the modular dual.
-
Symmetry TFTs for Continuous Spacetime Symmetries
Continuous spacetime symmetries can be encoded in a (d+1)-dimensional BF/Chern-Simons topological field theory, whose boundary reproduces symmetry generators, symmetry breaking, and anomalies.
-
Holographic Equidistribution
Equidistribution of Hecke operators in large N CFT limits reduces the partition function to light-state Poincaré series with an immediate interpretation as sums over handlebody geometries.
-
Self-dual monopole loops, instantons and confinement
Interactions among self-dual monopole-like constituents of instantons remove the infrared divergence and, the authors conjecture, drive confinement in 4d Yang-Mills.
-
$S$-duality, boundary states, and higher-form symmetries on ALE spaces
Maxwell theory on ALE spaces yields vector-valued modular boundary states whose gluing produces ordinary closed-manifold partition functions, with extensions to mixed electric-magnetic 1-form anomalies.
-
What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
Discussion (0). Continue with ORCID to comment.