Related papers: Instanton Geometry and Quantum A-infinity structur…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…
Instanton-dyons, also known as instanton-monopoles or instanton-quarks, are topological constituents of the instantons at nonzero temperature and nonzero expectation value of $A_4$. While the interaction between instanton-dyons has been…
In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded…
The present paper is the second part of our project in which we describe quantum field theories with instantons in a novel way by using the "infinite radius limit" (rather than the limit of free field theory) as the starting point. The…
The arcane ADHM construction of Yang-Mills instantons can be very naturally understood in the framework of D-brane dynamics in string theory. In this point-of-view, the mysterious auxiliary symmetry of the ADHM construction arises as a…
An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$,…
We discuss instantons on noncommutative four-dimensional Euclidean space. In commutative case one can consider instantons directly on Euclidean space, then we should restrict ourselves to the gauge fields that are gauge equivalent to the…
We investigate all the brane instanton solutions--an Einstein brane inhabiting at different positions in 5-dimensional negative curvature Einstein bulk. We construct a brane instanton model consisting of a brane with asymmetric bulk along…
We study the deformation theory of $\mathrm{G}_2$-instantons on nearly $\mathrm{G}_2$ manifolds. There is a one-to-one correspondence between nearly parallel $\mathrm{G}_2$ structures and real Killing spinors, thus the deformation theory…
We clarify certain aspects and discuss extensions of the recently introduced string D-instanton calculus (hep-th/0609191). The one-loop determinants are related to one-loop open string threshold corrections in intersecting D6-brane models.…
We investigate fundamental bounds on the curvature of quantum correlation functions in imaginary time. Focusing first on topological phases, we show that quantum geometry can qualitatively modify the imaginary-time decay of correlations,…
In this paper we study the geometry of manifolds with vector cross product and its complexification. First we develop the theory of instantons and branes and study their deformations. For example they are (i) holomorphic curves and…
We compute the A-infinity structure on the self-Ext algebra of the vector bundle $G$ over an elliptic curve of the form $G=\bigoplus_{i=1}^r P_i\oplus \bigoplus_{j=1}^s L_j$, where $(P_i)$ and $(L_j)$ are line bundles of degrees 0 and 1,…
On an oriented, compact, connected, real four-dimensional manifold, $M$, we introduce a topological Lagrangian gauge field theory with a Bogomol'nyi structure that leads to non-singular, finite-Action, stable solutions to the variational…
Explicit construction of the basic SU(2) anti-instantons over the multi-Taub--NUT geometry via the classical conformal rescaling method is exhibited. These anti-instantons satisfiy the so-called weak holonomy condition at infinity with…
Throughout this paper, we comprehensively study instantons with every kind of continuous conformal symmetry. Examples of these objects are hard to come by due to non-linear constraints. However, by applying previous work on moduli spaces,…
We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a…
We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma and point out some subtle relations with the complex structure on the orbifold. We consider generalized instanton equations on R^4/\Gamma which are BPS equations…