Topological Quantum Field Theory

By Gard Spreemann. 2009

188 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/f478ad3ebadefa6eb7a5007c87fb5240e22d94bb

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Citations in the corpus

Zakopane lectures on loop gravity (2011, methodology): “In Atiyah’s scheme, an (n+ 1)-dimensional TQFT is as a functorial association of a finite dimensional Hilbert space HΓ to each closed oriented n-manifold Γ, and a vector WC ∈ HΓ to each oriented (n+ 1)-manifold C having Γ as its boundary [80, 81].”
Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops (2007, unknown): “Of course, in the twisted theory [1, 58] the problem does not arise, since ε is a scalar and can be set to be a non-zero constant everywhere.”
Fivebranes and Knots (2011, unknown): “This leads to a four-dimensional topological field theory by the same reasoning as in [85].”
Central charges of 𝒩 = 2 superconformal field theories in four dimensions (2008, methodology): “The best method for this purpose, valid for any four-manifold background, is to perform a topological twist of the N = 2 supersymmetry [21].”
The omega deformation, branes, integrability and Liouville theory (2010, background): “7) are the standard conditions that characterize the supersymmetry generator of a twisted four-dimensional topological field theory [35] that (in the case of SU(2) gauge theory without hypermultiplets) is related to Donaldson theory.”
Four-dimensional SCFTs from M5-branes (2012, background): “The twisted versions of supersymmetric field theories have been a subject of great interest and a source of many insights in physics and mathematics since their introduction [22].”
Twisted supersymmetric 5D Yang-Mills theory and contact geometry (2012, methodology): “This technique is an infinite dimensional generalization [11, 12] of the Atiyah-Bott-BerlineVergne localization theorem [13, 14], which we for completeness now briefly review.”
The structure of 2D semi-simple field theories (2007, methodology): “Thus, all Gromov-Witten classes GW ng , δ ∈ H • ( M ng ) are constructible from c 1 ( X ) and the quantum multiplication operator ( ξ · u ) at a single (semi-simple) point u .”
Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories (2012, background): “) In such theories, it is possible to compute F exactly via localization [22], which reduces the entire functional integral to a finite-dimensional matrix model [23-25].”
Exact results for five-dimensional superconformal field theories with gravity duals (2012, background): “The idea [1] is simple: pick a supercharge Q and add to the Lagrangian a Q-exact operator whose bosonic part is positive-definite.”
Localization techniques in quantum field theories (2016, methodology): “The Weil algebra Wg = R[g[1]⊕ g[2]] is an extension of the Chevalley-Eilenberg algebra CEg = R[g[1]] = Λg∨ by the algebra R[g[2]] = Sg∨ of symmetric polynomials on g CEg ←Wg ← Sg∨ (2.”
N$$ \mathcal{N} $$ = 1 supersymmetric indices and the four-dimensional A-model (2017, background): “In the case of N = 2 theories, one may also consider the fully topologically twisted partition function [47], which is naively a different object than the partial twist considered here.”