We elucidate certain aspects of F-theory gauge dynamics, due to quantum splitting of certain brane stacks, which are absent in the Type IIB limit. We also provide a working implementation of an algorithm for computing cohomology of line bundles on arbitrary toric varieties. This should be of general use for studying the physics of global Type IIB and F-theory models, in particular for the explicit counting of zero modes for rigid F-theory instantons which contribute to charged matter couplings. We illustrate the discussion by constructing and analyzing in detail a compact F-theory GUT model in which a D-brane instanton generates the top Yukawa coupling non-perturbatively.
Using D3/D(-1) brane set-up in type IIB string theory we introduce gauge-stringy instantons in N=2 U(N) supersymmetry theories with one matter multiplet in symmetric representation. In addition to the gauge and stringy moduli there exist extra zero modes that we refer to as "gauge-stringy" moduli. We show that the measure of the moduli space in this model becomes dimensionless for arbitary N when the gauge instanton charge k_g is equal to the stringy instanton charge k_s. This property of gauge-stringy instantons leads to having equal contributions from all instanton charges k_s=k_g=k in the e…
We argue that one can see a specific class of "stringy" D-instantons in the underlying 4D gauge theory as the UV completion of an ordinary gauge instanton of a completely broken gauge group corresponding to the "empty" cycle the D-instanton is located on. In this sense, the D-instanton induced non-perturbative superpotential can be qualitatively inferred directly from pure field-theory considerations.
D-instantons are used to probe the near-horizon geometry of D3-branes systems on orbifold spaces. For fractional D3-branes, D-instanton calculus correctly reproduces the gauge beta-function and U(1)_R anomaly of the corresponding N=2 non-conformal Super Yang-Mills theories. For D3-branes wrapping the orbifold singularity, D-instantons can be identified with gauge instantons on ALE space, providing evidence of AdS/CFT duality for gauge theories on curved spaces.
The effects of instantons close to the cut-off is studied in four dimensional SU(2) gauge theory with higher order derivative terms in the action. It is found in the framework of the dilute instanton gas approximation that the convergence of the topological observables requires non-universal beta function.
Semiclassical instanton solutions in the 3D SU(2) Georgi-Glashow model are transformed into the Weyl gauge. This illustrates the tunneling interpretation of these instantons and provides a smooth regularization of the singular unitary gauge. The 3D Georgi-Glashow model has both instanton and sphaleron solutions, in contrast to 3D Yang-Mills theory which has neither, and 4D Yang-Mills theory which has instantons but no sphaleron, and 4D electroweak theory which has a sphaleron but no instantons. We also discuss the spectral flow picture of fundamental fermions in a Georgi-Glashow instanton back…
A relation between the total instanton number and the quantum-numbers of magnetic monopoles that arise in general Abelian gauges in SU(2) Yang-Mills theory is established. The instanton number is expressed as the sum of the `twists' of all monopoles, where the twist is related to a generalized Hopf invariant. The origin of a stronger relation between instantons and monopoles in the Polyakov gauge is discussed.
The analysis in previous publications of the instanton constraints required to produce a finite action of the theory is carried out also for N=2 supersymmetric Yang-Mills theory.
Various string theory realizations of three-dimensional gauge theories relate them to gravitational instantons, Nahm equations and monopoles. We use this correspondence to model self-dual gravitational instantons of $D_k$-type as moduli spaces of singular monopoles, find their twistor spaces and metrics.
Systems of D3-branes at orientifold singularities can receive non-perturbative D-brane instanton corrections, inducing field theory operators in the 4d effective theory. In certain non-chiral examples, these systems have been realized as the infrared endpoint of a Seiberg duality cascade, in which the D-brane instanton effects arise from strong gauge theory dynamics. We present the first UV duality cascade completion of chiral D3-brane theories, in which the D-brane instantons arise from gauge theory dynamics. Chiral examples are interesting because the instanton fermion zero mode sector is to…
We refine a previous proposal for obtaining the multi-instanton partition function from the supersymmetric index of the 1d supersymmetric gauge theory on the worldline of D0-branes. We provide examples where the refinements are crucial for obtaining the correct result.
We study the super instanton solution in the gauge theory with U$(n_{+}| n_{-})$ gauge group. Based on the ADHM construction generalized to the supergroup theory, we derive the instanton partition function from the super instanton moduli space through the equivariant localization. We derive the Seiberg-Witten geometry and its quantization for the supergroup gauge theory from the instanton partition function, and study the connection with classical and quantum integrable systems. We also argue the brane realization of the supergroup quiver gauge theory, and possible connection to the non-superg…
We study instanton effects along the Coulomb branch of an N=2 supersymmetric Yang-Mills theory with gauge group SU(2) on Asymptotically Locally Euclidean (ALE) spaces. We focus our attention on an Eguchi-Hanson gravitational background and on gauge field configurations of lowest Chern class.
Using instanton calculus we check, in the weak coupling region, the nonperturbative relation $$ <\Trϕ^2>=iπ\left(\cf-{a\over 2} {\partial\cf\over\partial a}\right)$$ obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2 and turn out to agree with previous nonperturbative results.
We find semi-local fractional instantons of codimension four in Abelian and non-Abelian gauge theories coupled with scalar fields and the corresponding ${\mathbb C}P^{N-1}$ and Grassmann sigma models at strong gauge coupling. They are 1/4 BPS states in supersymmetric theories with eight supercharges, carry fractional (half) instanton charges characterized by the fourth homotopy group $π_4 (G/H)$, and have divergent energy in infinite spaces. We construct exact solutions for the sigma models and numerical solutions for the gauge theories. Small instanton singularity in sigma models is resolved …
In this contribution we describe how to obtain instanton effects in four dimensional gauge theories by computing string scattering amplitudes in D3/D(-1) brane systems. In particular we show that the disks with mixed boundary conditions, which are typical of the D3/D(-1) system, are the sources for the classical instanton solution.
N=1^* gauge theories are believed to have fractional instanton contributions in the confining vacua. D3 brane probe computations in gravitation dual of large-N N=2^* gauge theories point to the absence of such contributions in the low energy gauge dynamics. We study fractional instantons in N=2 SU(2) Yang-Mills theory from the field theoretical perspective. We present new solutions to the Seiberg-Witten SU(2) monodromy problem with the same perturbative asymptotic, a massless monopole and a dyon singularity on the moduli space, and fractional instanton corrections to N=2 prepotential in the se…
We study the fermionic zero modes around 1 instanton operators for 5d supersymmetric gauge theories of type USp, SO and the exceptional groups. The major motivation is to try to understand the global symmetry enhancement pattern in these theories.
We study the D3/D(-1) brane system and show how to compute instanton corrections to correlation functions of gauge theories in four dimensions using open string techniques. In particular we show that the disks with mixed boundary conditions that are typical of the D3/D(-1) system are the sources for the classical instanton solution. This can then be recovered from simple calculations of open string scattering amplitudes in the presence of D-instantons. Exploiting this fact we also relate this stringy description to the standard instanton calculus of field theory.
We show that there exist finite energy, non-singular instanton solutions for five-dimensional theories with broken gauge symmetry. The soliton is supported against collapse by a non-zero electric charge. The low-energy dynamics of these solutions is described by motion on the ADHM moduli space with potential.
We study N=2 supersymmetric Abelian gauge model with the Fayet-Iliopoulos term and an arbitrary number of chiral matter multiplets in two dimensions. By analyzing the instanton contribution we compute the non-perturbative corrections to the mass spectrum of the theory and the quantum deformation of the classical vacua space. In contrast to known examples the non-perturbative bosonic potential is saturated by the one-instanton contribution and can be directly found within the semiclassical expansion around the one-instanton saddle point.
We study IR-renormalon divergences in N=1 supersymmetric Yang Mills gauge theories and in two dimensional non linear sigma models with mass gap. We derive, in both types of theories, a direct connection between IR- renormalons and fractional instanton effects. From the point of view of large $N$ dualities we work out a connection between IR-renormalons and $c=1$ matrix models.
We study deformed supersymmetry in N=2 supersymmetric U(N) gauge theory in non(anti)commutative N=1 superspace. Using the component formalism, we construct deformed N=(1,1/2) supersymmetry explicitly. Based on the deformed supersymmetry, we discuss the C-dependence of the correlators. We also study the C-deformation of the instanton equation for the gauge group U(2).
A previous analysis of possible constraints of Yang-Mills instantons in the presence of spontaneous symmetry breaking is extended to supersymmetric QCD. It is again found that a constraint is necessary for the gauge field in second and fourth order of the gauge breaking parameter v. While the supersymmetric zero mode is well behaved to all orders, the lifted superconformal and quark zero modes show nonpermissible behaviour, but only at first order in v.
We consider evidence for the existence of gauge configurations with fractional charge in pure N=1 supersymmetric Yang-Mills theory . We argue that these field configurations are singular and have to be treated as distributions. It is shown that the path integral representation of constant Green's functions can be reduced to a finite dimensional integral. The fractional configurations are essentially the zero size limit of the usual instantons and they have a reduced number of fermionic zero modes. At the end we comment on the status of the D-instanton/YM-instanton correspondence within AdS/CFT…
We study the moduli spaces of self-dual instantons on CP^2 in a simple group G. When G is a classical group, these instanton solutions can be realised using ADHM-like constructions which can be naturally embedded into certain three dimensional quiver gauge theories with 4 supercharges. The topological data for such instanton bundles and their relations to the quiver gauge theories are described. Based on such gauge theory constructions, we compute the Hilbert series of the moduli spaces of instantons that correspond to various configurations. The results turn out to be equal to the Hilbert ser…
We discuss a string model where a conformal four-dimensional N=2 gauge theory receives corrections to its gauge kinetic functions from "stringy" instantons. These contributions are explicitly evaluated by exploiting the localization properties of the integral over the stringy instanton moduli space. The model we consider corresponds to a setup with D7/D3-branes in type I' theory compactified on T4/Z2 x T2, and possesses a perturbatively computable heterotic dual. In the heteoric side the corrections to the quadratic gauge couplings are provided by a 1-loop threshold computation and, under the …
We show that the BPS configurations of uniform field strength can be interpreted as those for sheets of infinite number of BPS magnetic monopoles, and found that the number of normalizable zero modes per each magnetic monopole charge is four. We identify monopole sheets as the intersecting planes of D3 branes. Similar analysis on self-dual instanton configurations is worked out and the number of zero modes per each instanton number is found to match that of single isolated instanton.
We study the non-perturbative effects induced by stringy instantons on N=2 SU}(N) gauge theories in four dimensions, realized on fractional D3 branes in a C^3/Z_3 orientifold. The stringy instantons, corresponding to D(-1) branes that occupy a node of the orientifold quiver diagram where no D3 brane is present, have the right content of zero-modes to produce non-perturbative terms in the four-dimensional effective action. In the SU(2) theory these terms have the same structure for all instanton numbers and yield a series of non-perturbative corrections to the prepotential. We explicitly comput…
We calculate instanton corrections to three dimensional gauge theories with N=4 and N=8 supersymmetry and SU(n) gauge groups. The N=4 results give new information about the moduli space of n BPS SU(2) monopoles, including the leading order non-pairwise interaction terms. A few comments are made on the relationship of the N=8 results to membrane scattering in matrix theory.
We derive a BPS-type bound for four-dimensional Born-Infeld action with constant B field background. The supersymmetric configuration saturates this bound and is regarded as an analog of instanton in U(1) gauge theory. Furthermore, we find the explicit solutions of this BPS condition. These solutions have a finite action proportional to the instanton number and represent D(p-4)-branes within a Dp-brane although they have a singularity at the origin. Some relations to the noncommutative U(1) instanton are discussed.
Abelian and center gauges are considered in continuum Yang-Mills theory in order to detect the magnetic monopole and center vortex content of gauge field configurations. Specifically we examine the Laplacian Abelian and center gauges, which are free of Gribov copies, as well as the center gauge analog of the (Abelian) Polyakov gauge. In particular, we study meron, instanton and instanton-anti-instanton field configurations in these gauges and determine their monopole and vortex content. While a single instanton does not give rise to a center vortex, we find center vortices for merons. Furtherm…
We analyze the vector multiplet prepotential of d=4, N=2 type IIA compactifications. We find that the worldsheet instanton corrections have a natural interpretation as one-loop corrections in five dimensions, with the extra dimension being compactified on a circle of radius $g_{s}\ell_{s}$. We argue that the relation between spacetime and worldsheet instantons is natural from this point of view. We also discuss the map between the type IIA worldsheet instantons and the spacetime instantons in the heterotic dual.
We calculate the leading weak-coupling instanton contribution to the moduli-space metric of N=2 supersymmetric Yang-Mills theory with gauge group SU(2) compactified on R^3 x S^1. The results are in precise agreement with the semiclassical expansion of the exact metric recently conjectured by Gaiotto, Moore and Neitzke based on considerations related to wall-crossing in the corresponding four-dimensional theory.
We derive the four dimensional N=1/2 super Yang-Mills theory from tree-level computations in RNS open string theory with insertions of closed string Ramond-Ramond vertices. We also study instanton configurations in this gauge theory and their ADHM moduli space, using systems of D3 and D(-1) branes in a R-R background.
Although all interactions in the Standard Model generate nonzero shifts of the vacuum energy and pressure, gravity does not interact with them. Assuming (i) that the reason why it is so breaks down at some scale $M_g$ and that (ii) the instanton-induced shifts at such scale generate the observed cosmological constant, we found that it then should happen at a (surprisingly small) scale $M_g\sim 10^3 TeV$.
Supersymmetric gauge theories in five dimensions often exhibit less symmetry than the ultraviolet fixed points from which they flow. The fixed points might have larger flavor symmetry or they might even be secretly six-dimensional theories on S^1. Here we provide a simple criterion when such symmetry enhancement in the ultraviolet should occur, by a direct study of the fermionic zero modes around one-instanton operators.
We study the relation between stringy instantons and strong dynamics effects in type IIB toric quiver gauge theories. By exploiting the involutive property of Seiberg duality we relate the classical constraint on the moduli space of the gauge theory with the stringy instanton contribution to the superpotential. The result holds for unitary, orthogonal and symplectic gauge groups.
We show how to construct the general action coupling (multi)instantons to gauge theories arising from branes probing arbitrary toric singularities. We give a general set of rules for how to construct such an action given the knowledge of the superpotential for the gauge theory. The main idea is to obtain the action by higgsing a theory whose instanton dynamics is known, namely an orbifold of N=4 super Yang-Mills. We find that the couplings of the fermionic zero-modes with the holomorphic fields are dictated by the structure of the superpotential describing the toric singularity. We present exp…
We show that supersymmetric gauge theories with a product gauge group admit quasi-instantons, which, like instantons, sit at the absolute minimum of the action in the corresponding topological sector. However, unlike ordinary instantons which preserve part of the supersymmetry, these break all supersymmetries of the action. We also provide a generalization where quasi-instantons take value in the associated Lie algebra of the recently proposed 3-algebras. When the structure constants and the metric of the algebra are covariantly constant, the gauge bundle admits new topological sectors with qu…
We discuss the contribution of ADHM multi-instantons to the higher-derivative terms in the gradient expansion along the Coulomb branch of N=2 and N=4 supersymmetric SU(2) gauge theories. In particular, using simple scaling arguments, we confirm the Dine-Seiberg nonperturbative nonrenormalization theorems for the 4-derivative/8-fermion term in the two finite theories (N=4, and N=2 with N_F=4).
The ADHM constraints which implicitly specify instanton gauge field configurations are solved for the explicit general form of instantons with topological charge two and gauge group U(N).
We discuss the Bosonic sector of a class of supersymmetric non-Lorentzian five-dimensional gauge field theories with an $SU(1,3)$ conformal symmetry. These actions have a Lagrange multiplier which imposes a novel $Ω$-deformed anti-self-dual gauge field constraint. Using a generalised 't Hooft ansatz we find the constraint equation linearizes allowing us to construct a wide class of explicit solutions. These include finite action configurations that describe worldlines of anti-instantons which can be created and annihilated. We also describe the dynamics on the constraint surface.
We give a detailed microscopic derivation of gauge and stringy instanton generated superpotentials for gauge theories living on D3-branes at Z_3-orientifold singularities. Gauge instantons are generated by D(-1)-branes and lead to Affleck, Dine and Seiberg (ADS) like superpotentials in the effective N=1 gauge theories with three generations of bifundamental and anti/symmetric matter. Stringy instanton effects are generated by Euclidean ED3-branes wrapping four-cycles on T^6/\Z_3. They give rise to Majorana masses in one case and non-renormalizable superpotentials for the other cases. Finally w…
One-loop corrections to the gauge coupling and the gauge kinetic function in certain classes of four-dimensional D-brane models are computed. It is described how to determine D-instanton corrections to the superpotential and the gauge kinetic function in such models. The Affleck-Dine-Seiberg superpotential is rederived in string theory. The existence of a new class of multi-instantons, dubbed poly-instantons, is conjectured.
We give a pedagogical introduction to D-brane instanton effects in vacuum configurations with open and unoriented strings. We focus on quiver gauge theories for unoriented D-branes at orbifold singularities and describe in some detail the Z_3 case, where both `gauge' and `exotic' instantons can generate non-perturbative super potentials, and the Z_5 case, where supersymmetry breaking may arise from the combined effect of `gauge' instantons and a FI D-term.
Following work on theories with SU(N) gauge groups, we perform a large-N saddle-point approximation of the measure for ADHM multi-instantons in N=4 supersymmetric gauge theories with symplectic or orthogonal gauge groups. For Sp(N) we find that a saddle-point only exists in the even instanton charge sector. For either Sp(N) or SO(N) the saddle-point solution parametrizes AdS_5 x RP^5, the dual supergravity geometry in the AdS/CFT correspondence for these theories. The instanton measure at large-N has the form of the partition function of ten-dimensional N=1 supersymmetric gauge theory with a u…
We use the exact instanton expansion to illustrate various string characteristics of noncommutative gauge theory in two dimensions. We analyse the spectrum of the model and present some evidence in favour of Hagedorn and fractal behaviours. The decompactification limit of noncommutative torus instantons is shown to map in a very precise way, at both the classical and quantum level, onto fluxon solutions on the noncommutative plane. The weak-coupling singularities of the usual Gross-Taylor string partition function for QCD on the torus are studied in the instanton representation and its double …
We discuss instanton operators in five-dimensional gauge theories. These are defined as disorder operators which create a non-vanishing second Chern class on a four-sphere surrounding their insertion point. As such they may be thought of as higher-dimensional analogues of three-dimensional monopole (or `t Hooft) operators. We argue that they play an important role in the enhancement of the Lorentz symmetry for maximally supersymmetric Yang-Mills to SO(1,5) at strong coupling.
We investigate quantum effects on the Coulomb branch of three-dimensional N=4 supersymmetric gauge theory with gauge group SU(2). We calculate perturbative and one-instanton contributions to the Wilsonian effective action using standard weak-coupling methods. Unlike the four-dimensional case, and despite supersymmetry, the contribution of non-zero modes to the instanton measure does not cancel. Our results allow us to fix the weak-coupling boundary conditions for the differential equations which determine the hyper-Kahler metric on the quantum moduli space. We confirm the proposal of Seiberg a…
The multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. Expressions can be notably simplified by the appropriate gauge transformation. This generates the compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating connection are irrelevant for physics but affect gauge dependent quantities.
The explicit multi-instanton solutions by 'tHooft and Jackiw, Nohl & Rebbi are generalized to curvilinear coordinates. The idea is that a gauge transformation can notably simplify the expressions obtained after the change of variables. The gauge transform generates a compensating addition to the gauge potential of pseudoparticles. Singularities of the compensating field are irrelevant for physics but may affect gauge dependent quantities.
This paper contains the results of our investigations of BPS instantons and of our work on N=2 supersymmetric gauge theories. The BPS instantons we study appear in type II string theory compactifications on Calabi-Yau threefolds. In the corresponding four-dimensional effective supergravity actions the BPS instantons arise as finite action solutions to the Euclidean equations of motion. For N=2 supersymmetric gauge theories we construct general Lagrangians involving gauge groups with (non-abelian) electric and magnetic (dyonic) charges. In this work a coupling to hypermultiplets is included.
