New theory couples Chern-Simons to matter, topological.
problem Developing a new topological theory in 3D.
method Coupling Chern-Simons to matter, using transverse holomorphic foliation.
result The theory is equivalent to an N=2 supersymmetric Chern-Simons matter theory.
Unified boundary conditions lead to supergroup WZW models.
problem Boundary conditions in topologically twisted Chern-Simons matter theories.
method Unified complexified gauge invariant boundary conditions.
result Low-energy effective field theories on M2-M5 intersections are supergroup WZW models.
The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.
problem Constructing geometrically 3d N=2 gauge theories.
method Using surgeries and M5-branes wrapping on plumbing three-manifolds.
result Various dualities of 3d theories can be interpreted as Kirby moves and equivalent surgeries.
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver bundles, and show that the reduced quiver gauge theories are all generically buil…
We identify a large class R of three-dimensional N=2 superconformal field theories. This class includes the effective theories T_M of M5-branes wrapped on 3-manifolds M, discussed in previous work by the authors, and more generally comprises theories that admit a UV description as abelian Chern-Simons-matter theories w…
Proves symmetries of extremal horizons in spacetimes.
problem Proving symmetries of extremal horizons in arbitrary dimensions.
method Analyzes Killing vector fields and near-horizon geometry.
result Enhanced isometry groups and shifted Aretakis instability.
New non-singular spacetimes found with negative cosmological constant.
problem Finding non-singular spacetimes with a negative cosmological constant.
method Constructing infinite-dimensional families of solutions to complex equations.
result Infinite-dimensional families of non-singular stationary space-times with negative cosmological constant.
It is postulated that quantum gravity is a sum over causal structures coupled to matter via scale evolution. Quantized causal structures can be described by studying simple matrix models where matrices are replaced by an algebra of quantum mechanical observables. In particular, previous studies constructed quantum grav…
New approach connects 3D Chern-Simons theory to spectral networks.
problem Understanding Chern-Simons invariants in 3D manifolds.
method Constructing equivalences between bundles and spectral networks.
result New formulas for Chern-Simons invariants of 3D manifolds.
Lecture notes on Lie groups and Chern-Simons theory for grad students.
problem Understanding Chern-Simons theory and its applications.
method Explains Lie groups and their relation to Chern-Simons theory.
result Motivated new fields in knot theory and topology.
Arithmetic Dijkgraaf-Witten theory constructs analogues in Chern-Simons TQFT.
problem Developing arithmetic analogues in Chern-Simons TQFT.
method Constructing arithmetic analogues of Chern-Simons 1-cocycle, prequantization bundle, and Chern-Simons functional.
result Decomposition and gluing formulas for arithmetic Chern-Simons invariants and arithmetic Dijkgraaf-Witten partition functions.
Chern-Simons theory on Seifert 3-manifolds evaluated.
problem Evaluating Chern-Simons theory on complex 3-manifolds.
method Abelianisation, background field method, Kawasaki Index theorem.
result Partition function evaluated on general Seifert 3-manifolds.
Teichmüller TQFT upgraded to level N, linked to quantum Chern-Simons Theory.
problem Constructing a Teichmüller TQFT at level N.
method Using results from [AK1] and [AK3], relating to quantum Chern-Simons Theory.
result Teichmüller TQFT at level N is connected to quantum Chern-Simons Theory.
Classifies extended Abelian Chern-Simons theories using quadratic modules.
problem Classifying extended Abelian Chern-Simons theories.
method Using quadratic modules to classify theories.
result Finite quadratic modules classify extended Abelian Chern-Simons theories.
The paper explores the connection between 3d gravity and Chern-Simons theory using affine group connections.
problem Exploring the relationship between 3d gravity and Chern-Simons theory.
method A variational problem of Chern-Simons type on a principal fiber bundle with general affine group structure is studied. The connection is established through a generalized notion of extension and reduction of connections.
result Established a correspondence between 3d gravity and Chern-Simons theory using affine group connections.
Proposes Teichmüller TQFT as a Chern-Simons theory with a new integration cycle.
problem Defining Teichmüller TQFT as a Chern-Simons theory with a novel integration cycle.
method Analytically continues Chern-Simons path-integral with an unusual integration cycle.
result Teichmüller TQFT is dual to complex SL(2,C) Chern-Simons theory at integer level k=1.
We study S-dualities in analytically continued SL(2) Chern-Simons theory on a 3-manifold M. By realizing Chern-Simons theory via a compactification of a 6d five-brane theory on M, various objects and symmetries in Chern-Simons theory become related to objects and operations in dual 2d, 3d, and 4d theories. For example,…
Categorifies Stokes coefficients in Chern-Simons theory models.
problem Stokes phenomenon in Chern-Simons theory around flat connections.
method Finite-dimensional model for analytically continued Chern-Simons theory, categorification of Stokes coefficients.
result Stokes coefficients can be promoted to graded vector spaces.
We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this Fermionic theory gives rise to a convergent perturbation expansion. This leads us to c…
Chern-Simons and Reshetikhin-Turaev theories are shown equivalent for U(1) gauge group.
problem Equivalence between U(1) Chern-Simons and Reshetikhin-Turaev TQFTs. method Proof of natural isomorphism between theories for finite quadratic modules.
result Extended (2+1)-dimensional TQFTs are naturally isomorphic. Study evaluates Chern-Simons theory on Seifert fibred 3-manifolds.
problem Evaluate Chern-Simons theory on Seifert fibred 3-manifolds.
method Use Abelianisation method to evaluate the partition function and Wilson loops.
result Obtain closed formulae for expectation values of torus knots.
Study of U(1) gauge theories on G2 manifolds, including instantons and Chern-Simons.
problem Investigate U(1) gauge theories on G2 manifolds. method Analyze U(1)-Yang-Mills and higher-order U(1)-Chern-Simons theories on G2 manifolds. result Emergence of G2 manifolds from anti-self-dual U(1) instantons and calculation of partition functions. Explains a new method for quantizing field theories with boundaries.
problem Quantizing field theories on manifolds with boundaries.
method BV-BFV formalism for perturbative quantization.
result Demonstrates Chern-Simons theory as a new example.
In a previous paper we constructed classical spin Chern-Simons for any compact Lie group G: a gauge theory whose action depends on the spin structure of the 3-manifold. Here we apply geometric quantization to the classical Hamiltonian theory and investigate the formal properties of the partition function in the Lagra…
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
Non-trivial obstructions found for topological solitons in Yang-Mills-Chern-Simons theories.
problem Existence of topological solitons in Yang-Mills-Chern-Simons theories on compact manifolds.
method Cohomological formulations of the calculus of variations, focusing on Yang-Mills-Chern-Simons theories on compact manifolds in odd dimensions.
result Non-trivial obstructions leading to a strong non-existence theorem for topological solitons.
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has served as a key example in understanding the structure of TQFTs in general. We su…
Diagrammatic method calculates knot invariant related to Chern-Simons theory.
problem Calculating knot invariants in Chern-Simons theory.
method Diagrammatic approach for compact oriented 3-manifolds.
result Diagrammatic method for computing knot invariant d. Chern-Simons and Reshetikhin-Turaev theories are shown equivalent.
problem Equivalence of two quantum field theories.
method Geometric quantization and modular categories.
result Toral Chern-Simons theory is isomorphic to Reshetikhin-Turaev theory.
Study on resurgence in Chern-Simons theory, recovering flat connection contributions.
problem Understanding the resurgence properties of Chern-Simons theory partition functions.
method Analyzing Borel transforms and asymptotic expansions of partition functions.
result Recovery of irreducible flat connection contributions from abelian flat connections.
We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which co…
Computes entanglement entropy using Chern-Simons theory and symmetric webs.
problem Determining if a product state implies unlinked components.
method Using symmetric webs to compute colored link invariants and write multi-partite entangled states.
result Written down multi-partite entangled states of any given link.
Geometrically constructs dilogarithm from Chern-Simons theory.
problem Dilogarithm function and its properties.
method Spin Chern-Simons invariant of C*-connections.
result Geometric proofs of dilogarithm identities and branching structure.
Chern-Weil theory provides for each invariant polynomial on a Lie algebra g a map from g-connections to differential cocycles whose volume holonomy is the corresponding Chern-Simons theory action functional. Kotov and Strobl have observed that this naturally generalizes from Lie algebras to dg-manifolds and dg-bundles …
We test the 3d-3d correspondence for theories that are labelled by Lens spaces. We find a full agreement between the index of the 3d N=2 "Lens space theory" T[L(p,1)] and the partition function of complex Chern-Simons theory on L(p,1). In particular, for p=1, we show how the familiar S3 partition func…
We formulate a refinement of SU(N) Chern-Simons theory on a three-manifold via the refined topological string and the (2,0) theory on N M5 branes. The refined Chern-Simons theory is defined on any three-manifold with a semi-free circle action. We give an explicit solution of the theory, in terms of a one-parameter refi…
Formula calculates invariant for 3-manifolds with torus boundaries.
problem Calculating an invariant for 3-manifolds with torus boundaries.
method Generalized Chern-Simons invariant and provided a gluing formula.
result A gluing formula for the invariant d(M,ρ). Resurgence analysis of SU(2) Chern-Simons on a specific homology sphere.
problem Analyzing the resurgence of a specific Chern-Simons partition function.
method Borel resummation of the perturbative expansion of an exact partition function.
result Resurgence analysis reveals new insights into the partition function.
This paper quantizes geometry using SL(2,C) Chern-Simons theory and flat connections.
problem Quantizing four-dimensional quantum geometry.
method Using a correspondence between flat connections and four-dimensional simplices, the paper quantizes geometry via complex SL(2,C) Chern-Simons theory.
result The quantum geometrical states are represented by the 3d blocks of analytically continued Chern-Simons theory, and in the semiclassical limit, the three-dimensional Chern-Simons action becomes the discrete Einstein-Hilbert action of a 4-simplex.
This work connects knot invariants to Chern-Simons theories via factorization homology.
problem Understanding knot invariants in Chern-Simons theories.
method Constructing a filtered E3-algebra and proving an equality between factorization homology trace and Reshetikhin-Turaev link invariant. result Established a connection between knot invariants and Chern-Simons theories.
We extend finite dimensional Chern-Simons theory to certain infinite dimensional principal bundles with connections, in particular to the frame bundle FLM→LM over the loop space of a Riemannian manifold M. Chern-Simons forms are defined roughly as in finite dimensions with the invariant polynomials replaced by a…
The first part of this text is a gentle exposition of some basic constructions and results in the extended prequantum theory of Chern-Simons-type gauge field theories. We explain in some detail how the action functional of ordinary 3d Chern-Simons theory is naturally localized ("extended", "multi-tiered") to a map on t…
Chern-Simons theory on a closed contact three-manifold is studied when the Lie group for gauge transformations is compact, connected and abelian. A rigorous definition of an abelian Chern-Simons partition function is derived using the Faddeev-Popov gauge fixing method. A symplectic abelian Chern-Simons partition functi…
Mathematical construction of Chern-Simons partition function using reflection positivity.
problem Constructing a mathematical framework for Chern-Simons functional integrals.
method Reflection positive functional on Banach space of connections, unitary operators, weak limit.
result Nonperturbative construction of partition function without renormalization.
New method calculates Chern-Simons volume for 3-manifolds with surgery diagrams.
problem Computing Chern-Simons volume for 3-manifolds with torus boundaries and cusps.
method Direct computation from surgery diagrams using a log-decoration and quantum group coordinates.
result Direct computation of Chern-Simons volume for 3-manifolds with torus boundaries and cusps.
Hennings and Chern-Simons invariants match for certain quantum groups.
problem Matching invariants for quantum groups and Chern-Simons theory.
method Comparing invariants for arbitrary simple Lie algebras at roots of unity.
result Agreement of Hennings and Chern-Simons invariants for integer homology three-spheres.
We introduce certain relative differential characters which we call Cheeger-Chern-Simons characters. These combine the well-known Cheeger-Simons characters with Chern-Simons forms. In the same way as the Cheeger-Simons characters generalize Chern-Simons invariants of oriented closed manifolds, the Cheeger-Chern-Simons …
The volume conjecture is extended to all orders for hyperbolic 3-manifolds using complex Chern-Simons theory.
problem Extending the volume conjecture to all orders for hyperbolic 3-manifolds.
method Deriving formulas for the perturbative expansion of the partition function of complex Chern-Simons theory and comparing it to Witten-Reshetikhin-Turaev invariants.
result The conjecture that the perturbative expansion of the partition function of complex Chern-Simons theory matches the Witten-Reshetikhin-Turaev invariants at roots of unity in the limit of infinitely many invariants.