We describe the infinitesimal moduli space of pairs $(Y, V)$ where $Y$ is a manifold with $G_2$ holonomy, and $V$ is a vector bundle on $Y$ with an instanton connection. These structures arise in connection to the moduli space of heterotic string compactifications on compact and non-compact seven dimensional spaces, e.g. domain walls. Employing the canonical $G_2$ cohomology developed by Reyes-Carrión and Fernández and Ugarte, we show that the moduli space decomposes into the sum of the bundle moduli $H^1_{\check{d}_A}(Y,\mathrm{End}(V))$ plus the moduli of the $G_2$ structure preserving the instanton condition. The latter piece is contained in $H^1_{\check{d}_θ}(Y,TY)$, and is given by the kernel of a map ${\cal\check F}$ which generalises the concept of the Atiyah map for holomorphic bundles on complex manifolds to the case at hand. In fact, the map ${\cal\check F}$ is given in terms of the curvature of the bundle and maps $H^1_{\check{d}_θ}(Y,TY)$ into $H^2_{\check{d}_A}(Y,\mathrm{End}(V))$, and moreover can be used to define a cohomology on an extension bundle of $TY$ by $\mathrm{End}(V)$. We comment further on the resemblance with the holomorphic Atiyah algebroid and connect the story to physics, in particular to heterotic compactifications on $(Y,V)$ when $α'=0$.
We investigate Yang-Mills instantons on a 7-dimensional manifold of G_2 holonomy. By proposing a spherically symmetric ansatz for the Yang-Mills connection, we have ordinary differential equations as the reduced instanton equation, and give some explicit and numerical solutions.
Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. Seven-dimensional spaces with G_2 holonomy fibered over the Taub-Nut and the Eguchi-Hanson gravitational instantons are found, together with other examples. By considering the Apostolov-Salamon theorem math.DG/0303197, we construct a new example that, still being a T^2 bundle over hyper-Kahler, represents a non trivial two parameter deformation of the metrics studied in hep-th/010819…
We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed by Harland and Nolle in such a way that instantons are parameterized by constrained matrix-valued functions. Our ansatz reduces instanton equations to a matrix model equations which can be further reduced to Newtonian mechanics with particle trajectories obeying first-order gradient flow equations. Generalizations to Kaehler-Einstein manif…
We calculate exactly the functional determinant for fermions in fundamental representation of SU(2) in the background of periodic instanton with non-trivial value of the Polyakov line at spatial infinity. The determinant depends on the value of the holonomy v, the temperature, and the parameter r_12, which at large values can be treated as separation between the Bogomolny--Prasad--Sommerfeld monopoles (or dyons) which constitute the periodic instanton. We find a compact expression for small and large r_12 and compute the determinant numerically for arbitrary r_12 and v.
The holonomy of an SU(2) N-instanton in the x^4-direction gives a map from R^3 into SU(2), which provides a good model of an N-Skyrmion. Combining this map with the standard Hopf map from SU(2)=S^3 to S^2 gives a configuration for a Hopf soliton of charge N. In this way, one may define a collective-coordinate manifold for Hopf solitons. This paper deals with instanton approximations to Hopf solitons in the Skyrme-Faddeev model, focussing in particular on the N=1 and N=2 sectors, and the two-soliton interaction.
The total space of the spinor bundle on the four dimensional sphere S^4 is a quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider octonionic Yang-Mills instanton on this eight dimensional gravitational instanton. This is a higher dimensional generalization of (anti-)self-dual instanton on the Eguchi-Hanson space. We propose an ansatz for Spin(7) Yang-Mills field and derive a system of non-linear ordinary differential equations. The solutions are classified according to the asymptotic behavior at infinity. We give a complete solution, when the gauge group is reduced to…
We calculate exactly functional determinants for quantum oscillations about periodic instantons with non-trivial value of the Polyakov line at spatial infinity. Hence, we find the weight or the probability with which calorons with non-trivial holonomy occur in the Yang--Mills partition function. The weight depends on the value of the holonomy, the temperature, Lambda_QCD, and the separation between the BPS monopoles (or dyons) which constitute the periodic instanton. At large separation between constituent dyons, the quantum measure factorizes into a product of individual dyon measures, times …
We present the detailed derivation of the charge one periodic instantons - or calorons - with non-trivial holonomy for SU(2). We use a suitable combination of the Nahm transformation and ADHM techniques. Our results rely on our ability to compute explicitly the relevant Green's function in terms of which the solution can be conveniently expressed. We also discuss the properties of the moduli space, R^3 X S^1 X Taub-NUT/Z_2 and its metric, relating the holonomy to the Taub-NUT mass parameter. We comment on the monopole constituent description of these calorons, how to retrieve topological charg…
Following the work of Lima et al on the exact evaluation of the nonperturbative contribution to the superpotential from open-membrane instanton in Heterotic M-Theory, we evaluate systematically the contribution to the superpotential of a membrane instanton obtained by wrapping of a single M2 brane, once, on an isolated supersymmetric 3-cycle in a G_2-holonomy manifold. We then try to relate the results obtained to those sketched out in Harvey and Moore. We also do a heat-kernel asymptotics analysis to see whether one gets similar UV-divergent terms for (one or both of) the bosonic and fermioni…
By explicit construction of the ADHM data, we prove the existence of a charge seven instanton with icosahedral symmetry. By computing the holonomy of this instanton we obtain a Skyrme field which approximates the minimal energy charge seven Skyrmion. We also present a one parameter family of tetrahedrally symmetric instantons whose holonomy gives a family of Skyrme fields which models a Skyrmion scattering process, where seven well-separated Skyrmions collide to form the icosahedrally symmetric Skyrmion.
We show that Skyrmions with massless pions in hyperbolic space provide a good approximation to Skyrmions with massive pions in Euclidean space, for a particular relationship between the pion mass and the curvature of hyperbolic space. Using this result we describe how a Skyrmion with massive pions in Euclidean space can be approximated by the holonomy along circles of a Yang-Mills instanton. This is a generalization of the approximation of Skyrmions by the holonomy along lines of an instanton, which is only applicable to massless pions.
We study Ricci-flat metrics on non-compact manifolds with the exceptional holonomy $Spin(7), G_2$. We concentrate on the metrics which are defined on ${\bf R} \times G/H$. If the homogeneous coset spaces $G/H$ have weak $G_2$, SU(3) holonomy, the manifold ${\bf R} \times G/H$ may have $Spin(7), G_2$ holonomy metrics. Using the formulation with vector fields, we investigate the metrics with $Spin(7)$ holonomy on ${\bf R}\times Sp(2)/Sp(1), {\bf R}\times SU(3)/U(1)$. We have found the explicit volume-preserving vector fields on these manifold using the elementary coordinate parameterization. Thi…
The functional determinant is computed exactly for quantum oscillations about periodic instantons with non-trivial values of the Polyakov line at spatial infinity (or holonomy). Such instantons can be viewed as composed of the Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the weight or the probability with which dyons occur in the pure Yang--Mills partition function. It turns out that dyons experience quantum interactions having the familiar "linear plus Coulomb" form but with the "string tension'' depending on the holonomy. We present an argument that at temperatures below …
We consider the non-perturbative superpotential for a class of four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are so-called twisted connected sum (TCS) constructions, which have the topology of a K3-fibration over $S^3$. We show that the non-perturbative superpotential of M-theory on a class of TCS geometries receives infinitely many inequivalent M2-instanton contributions from infinitely many three-spheres, which we conjecture are supersymmetric (and thus associative) cycles. The rationale …
We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits $U(1)^3$ gauge symmetry and a spectrum of massive charged particles that includes a trifundamental. Applying recent mathematical results to this example, we compute membrane instanton corrections to the superpotential and spacetime topology change in a compact model; the latter include both the (non-isolated) $G_2$ flo…
Calorons of the SU(N) gauge group with non-trivial holonomy, i.e. periodic instantons with arbitrary eigenvalues of the Polyakov line at spatial infinity, can be viewed as composed of N Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. Using the metric of the caloron moduli space found previously we compute the integration measure over caloron collective coordinates in terms of the constituent monopole positions and their U(1) phases. In the limit of small separations between dyons and/or trivial holonomy, calorons reduce locally to the standard instantons whose traditional collective c…
We review results of the last two years concerning caloron solutions of unit charge with non-trivial holonomy, revealing the constituent monopole nature of these instantons. For SU(n) there are n such BPS constituents. New is the presentation of the exact values for the Polyakov loop at the three constituent locations for the SU(3) caloron with arbitrary holonomy. At these points two eigenvalues coincide, extending earlier results for SU(2) to a situation more generic for general SU(n).
We consider $G_2$-structures with torsion coupled with $G_2$-instantons, on a compact $7$-dimensional manifold. The coupling is via an equation for $4$-forms which appears in supergravity and generalized geometry, known as the Bianchi identity. First studied by Friedrich and Ivanov, the resulting system of partial differential equations describes compactifications of the heterotic string to three dimensions, and is often referred to as the $G_2$-Strominger system. We study the moduli space of solutions and prove that the space of infinitesimal deformations, modulo automorphisms, is finite dime…
Necessary and sufficient conditions to the existence of a hermitian connection with totally skew-symmetric torsion and holonomy contained in SU(3) are given. Non-compact solution to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton is found in dimensions 6. Non-conformally flat non-compact solutions to the supergravity-type I equations of motion with non-zero flux and non-constant dilaton are found in dimensions 7 and 8. A Riemannian metric with holonomy contained in $G_2$ arises from our considerations and Hitchin's flow equations, which seems to be new. …
We present a unified eight-dimensional approach to instanton equations on several seven-dimensional manifolds associated to a six-dimensional homogeneous nearly Kähler manifold. The cone over the sine-cone on a nearly Kähler manifold has holonomy group Spin(7) and can be foliated by submanifolds with either holonomy group G_2, a nearly parallel G_2-structure or a cocalibrated G_2-structure. We show that there is a G_2-instanton on each of these seven-dimensional manifolds which gives rise to a Spin(7)-instanton in eight dimensions. The well-known octonionic instantons on R^7 and R^8 are contai…
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 respect to the trivial flat connection and decay rapidly. The resulting unital energy anti-instantons have trivial holonomy at infinity. We also fully describe their unframed moduli space and find that it is a five dimensional space admitting a singular disk-fibration over R^3. On the way, we work out in detail the twistor space of the multi-Taub--NUT geometry t…
In this Letter we establish a relationship between symmetric SU(2) Yang--Mills instantons and metrics with Spin(7)-holonomy. Our method is based on a slight extension of that of Bryant and Salamon developed to construct explicit manifolds with special holonomies in 1989. More precisely, we prove that making use of symmetric SU(2) Yang--Mills instantons on Riemannian spin-manifolds, we can construct metrics on the chiral spinor bundle whose holonomies are within Spin(7). Moreover if the resulting space is connected, simply connected and complete, the holonomy coincides with Spin(7). The basic e…
In this note I review the construction of higher-dimensional instantons and heterotic NS5-branes on Ricci-flat cones from arXiv:1109.3552, as well as fractional strings from arXiv:1202.5046. The focus is on methods and interpretation. I show, furthermore, that smeared 5-brane supergravity solutions on manifolds with holonomy G2 or Spin(7) can be obtained quite generally by a conformal deformation of the Ricci-flat metric, whereas Calabi-Yau and hyperkähler manifolds require more sophisticated deformations and a case by case treatment.
For $M$-theory on the $G_2$ holonomy manifold given by the cone on ${\bf S^3}\x {\bf S^3}$ we consider the superpotential generated by membrane instantons and study its transformations properties, especially under monodromy transformations and triality symmetry. We find that the latter symmetry is, essentially, even a symmetry of the superpotential. As in Seiberg/Witten theory, where a flat bundle given by the periods of an universal elliptic curve over the $u$-plane occurs, here a flat bundle related to the Heisenberg group appears and the relevant universal object over the moduli space is re…
We discuss the higher dimensional generalization of gravitational instantons by using volume-preserving vector fields. We give special attention to the case of 8-dimensions and present a new construction of the Ricci flat metric with holonomy in Spin(7). An example of the metric is explicitly given. Further it is shown that our formulation has a natural interpretation in the Chern-Simons theory written by the language of superconnections.
We review the relations between a family of domain-wall solutions to M-theory and gravitational instantons with special holonomy. When oxidized into the maximal-dimension parent supergravity, the transverse spaces of these domain walls become cohomogeneity-one spaces with generalized Heisenberg symmetries and a homothetic conformal symmetry. These metrics may also be obtained as scaling limits of generalized Eguchi-Hanson metrics, or, with appropriate discrete identifications, from generalized Atiyah-Hitchin metrics, thus providing field-theoretic realizations of string-theory orientifolds.
We study the dynamics of M-theory on G2 holonomy manifolds, and consider in detail the manifolds realized as the quotient of the spin bundle over S^3 by discrete groups. We analyse, in particular, the class of quotients where the triality symmetry is broken. We study the structure of the moduli space, construct its defining equations and show that three different types of classical geometries are interpolated smoothly. We derive the N=1 superpotentials of M-theory on the quotients and comment on the membrane instanton physics. Finally, we turn on Wilson lines that break gauge symmetry and disc…
A 7-manifold with G_2 holonomy can be constructed as a R^3 bundle over a quaternionic space. We consider a quaternionic base space which is singular and its metric depends on three parameters, where one of them corresponds to an interpolation between S^4 and CP^2 or its non-compact analogs. This 4-d Einstein space has four isometries and the fixed point set of a generic Killing vector is discussed. When embedded into M-theory the compactification over a given Killing vector gives intersecting 6-branes as IIA configuration and we argue that membrane instantons may resolve the curvature singular…
We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these spaces introduced by Hausel--Hunsicker--Mazzeo. First referring to the codimension 2 singularity removal theorem of Sibner--Sibner and Rade we prove that given a smooth, finite energy, self-dual SU(2) connection over a complete ALF space, its energy is congruent to a Chern--Simons invariant of the boundary three-manifold if the connection satisfies a certain holo…
We consider the 6d superconformal field theory realized on M5-branes probing the $E_8$ end-of-the-world brane on the deformed and resolved $\mathbb{C}^2/\mathbb{Z}_k$ singularity. We give an explicit algorithm which determines, for arbitrary holonomy at infinity, the 6d quiver gauge theory on the tensor branch, the type-A class S description of the $T^2$ compactification, and the star-shaped quiver obtained as the mirror of the $T^3$ compactification.
We construct the space of infinitesimal variations for the Strominger system and an obstruction space to integrability, using elliptic operator theory. We initiate the study of the geometry of the moduli space, describing the infinitesimal structure of a natural foliation on this space. The associated leaves are related to generalized geometry and correspond to moduli spaces of solutions of suitable Killing spinor equations on a Courant algebroid. As an application, we propose a unifying framework for metrics with holonomy $\SU(3)$ and solutions of the Strominger system.
We investigate nonperturbative effects in M-theory compactifications arising from wrapped membranes. In particular, we show that in $d=4, \mathcal{N}=1$ compactifications along manifolds of $G_2$ holonomy, membranes wrapped on rigid supersymmetric 3-cycles induce nonzero corrections to the superpotential. Thus, membrane instantons destabilize many M-theory compactifications. Our computation shows that the low energy description of membrane physics is usefully described in terms of three-dimensional topological field theories, and the superpotential is expressed in terms of topological invarian…
We consider Yang-Mills theory on manifolds ${\mathbb R}\times X$ with a $d$-dimensional Riemannian manifold $X$ of special holonomy admitting gauge instanton equations. Instantons are considered as particle-like solutions in $d+1$ dimensions whose static configurations are concentrated on $X$. We study how they evolve in time when considered as solutions of the Yang-Millsequations on ${\mathbb R}\times X$ with moduli depending on time $t\in{\mathbb R}$. It is shown that in the adiabatic limit, when the metric in the $X$ direction is scaled down, the classical dynamics of slowly moving instanto…
We propose a construction of Skyrme fields from holonomy of the spin connection of gravitational instantons. The procedure is implemented for Atiyah-Hitchin and Taub-NUT instantons. The skyrmion resulting from the Taub-NUT is given explicitly on the space of orbits of a left translation inside the whole isometry group. The domain of the Taub-NUT skyrmion is a trivial circle bundle over the Poincare disc. The position of the skyrmion depends on the Taub-NUT mass parameter, and its topological charge is equal to two.
We present several results concerning non-commutative instantons and the Seiberg-Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang-Mills theory. These include the two dimensional ``shift operator'' solutions and the four dimensional Nekrasov-Schwarz instantons as special cases. We also study how the Seiberg-Witten map acts on these instanton solutions. The infinitesimal Seiberg-Witten map is shown to take a very simple form in operator language, and this result is used to give a commutative description of non-c…
The first irreducible solution of the $\mathrm{SU} (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later than the famous BPST instantons on $\mathbb{R}^4$ were discovered. While soon after, in 1978, the ADHM construction gave a complete description of the moduli spaces of instantons on $\mathbb{R}^4$, the case of the Euclidean Schwarzschild manifold has resisted many efforts for the past 40 years. By exploring a correspondence between the planar Abelian vortices and spherically symmetric instantons on ES, we obtain: a …
We construct nearly topological Yang-Mills theories on eight dimensional manifolds with a special holonomy group. These manifolds are the Joyce manifold with $Spin(7)$ holonomy and the Calabi-Yau manifold with SU(4) holonomy. An invariant closed four form $T_{μνρσ}$ on the manifold allows us to define an analogue of the instanton equation, which serves as a topological gauge fixing condition in BRST formalism. The model on the Joyce manifold is related to the eight dimensional supersymmetric Yang-Mills theory. Topological dimensional reduction to four dimensions gives non-abelian Seiberg-Witte…
Heterotic string compactifications on integrable $G_2$ structure manifolds $Y$ with instanton bundles $(V,A), (TY,\tildeθ)$ yield supersymmetric three-dimensional vacua that are of interest in physics. In this paper, we define a covariant exterior derivative $\cal D$ and show that it is equivalent to a heterotic $G_2$ system encoding the geometry of the heterotic string compactifications. This operator $\cal D$ acts on a bundle ${\cal Q}=T^*Y\oplus{\rm End}(V)\oplus{\rm End}(TY)$ and satisfies a nilpotency condition $\check{\cal D}^2=0$, for an appropriate projection of $\cal D$. Furthermore, …
In this paper, the metric on the moduli space of the k=1 SU(n) periodic instanton -or caloron- with arbitrary gauge holonomy at spatial infinity is explicitly constructed. The metric is toric hyperKaehler and of the form conjectured by Lee and Yi. The torus coordinates describe the residual U(1)^{n-1} gauge invariance and the temporal position of the caloron and can also be viewed as the phases of n monopoles that constitute the caloron. The (1,1,..,1) monopole is obtained as a limit of the caloron. The calculation is performed on the space of Nahm data, which is justified by proving the isome…
This note revisits recent results regarding the geometry and moduli of solutions of the heterotic string on manifolds $Y$ with a $G_2$ structure. In particular, such heterotic $G_2$ systems can be rephrased in terms of a differential $\check {\cal D}$ acting on a complex $\checkΩ^*(Y , {\cal Q})$, where ${\cal Q}=T^*Y\oplus{\rm End}(TY)\oplus{\rm End}(V)$ and $\check {\cal D}$ is an appropriate projection of an exterior covariant derivative ${\cal D}$ which satisfies an instanton condition. The infinitesimal moduli are further parametrised by the first cohomology $H^1_{\check {\cal D}}(Y,{\cal…
Phenomenological compactifications of M-theory involve 7-manifolds with G_2 holonomy and various singularities. Here we study local geometries with such singularities, by thinking of them as compactifications of 7d supersymmetric Yang-Mills theory on a three-manifold Q_3. We give a general discussion of compactifications of 7d Yang-Mills theory in terms of Higgs bundles on Q_3. We show they can be constructed using spectral covers, which are Lagrangian branes with a flat connection in the cotangent bundle T^*Q_3. We explain the dictionary with ALE fibrations over Q_3 and conjecture that these …
The worldvolume theory of D3-branes probing four D7-branes and an O7-plane on $\mathbb{C}^2/\mathbb{Z}_2$ is given by a supersymmetric USp x USp gauge theory. We demonstrate that, at least for a particular choice of the holonomy at infinity, we can go to a dual description of the gauge theory, where we can add a Fayet-Iliopoulos term describing the blowing-up of the orbifold to the smooth ALE space. This allows us to express the moduli space of SO(8) instantons on the smooth ALE space as a hyperkähler quotient of a flat space times the Higgs branch of a class S theory. We also discuss a genera…
We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metric connection with closed skew-symmetric torsion. We develop Hodge theory on such manifolds showing how the reduction of the holonomy group causes a decomposition of the twisted cohomology. For SKT manifolds this decomposition is accompanied by an identity between different Laplacian operators and forces the collapse of a spectral sequence at the first page. Further we study the deformation theory of SKT st…
We consider euclidean D-branes wrapping around manifolds of exceptional holonomy in dimensions seven and eight. The resulting theory on the D-brane---that is, the dimensional reduction of 10-dimensional supersymmetric Yang-Mills theory---is a cohomological field theory which describes the topology of the moduli space of instantons. The 7-dimensional theory is an N_T = 2 (or balanced) cohomological theory given by an action potential of Chern-Simons type. As a by-product of this method, we construct a related cohomological field theory which describes the monopole moduli space on a 7-manifold o…
The membrane instanton superpotential for $M$-theory on the $G_2$ holonomy manifold given by the cone on ${\bf S^3}\x {\bf S^3}$ is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.
We construct a flat (and fake-flat) 2-connection in the configuration space of $n$ indistinguishable particles in the complex plane, which categorifies the $sl(2,C)$-Knizhnik-Zamolodchikov connection obtained from the adjoint representation of $sl(2,C)$. This will be done by considering the adjoint categorical representation of the string Lie 2-algebra and the notion of an infinitesimal 2-Yang-Baxter operator in a differential crossed module. Specifically, we find an infinitesimal 2-Yang-Baxter operator in the string Lie 2-algebra, proving that any (strict) categorical representation of the st…
The main results presented in this dissertation are the following - We have shown that in $d=4$ weak hyperkahler torsion structures are the same that hypercomplex structures and the same that the Plebanski-Finley conformally invariant heavens. With the help of this identification we have found the most general local form of an hyperkahler torsion space in four dimensions. We also presented an Ashtekar like formulation for them in which to finding an hyperkahler torsion metric is reduced to solve a quadratic differential system. - It is found the most general form for the target space metric to…
Pure Yang-Mills instantons are considered on S^1 x R^3 -- so-called calorons. The holonomy -- or Polyakov loop around the thermal S^1 at spatial infinity -- is assumed to be a non-centre element of the gauge group SU(n) as most appropriate for QCD applications in the confined phase. It is shown that a charge k caloron can be seen as a collection of nk massive magnetic monopoles each carrying fractional topological charge. This interpretation offers a physically appealing way of introducing monopole degrees of freedom into pure gluodynamics: as constituents of finite temperature instantons. New…
We study moduli stabilization in the context of M-theory on compact manifolds with G2 holonomy, using superpotentials from flux and membrane instantons, and recent results for the Khaeler potential of such models. The existence of minima with negative cosmological constant, stabilizing all moduli, is established. While most of these minima preserve supersymmetry, we also find examples with broken supersymmetry. Supersymmetric vacua with vanishing cosmological constant can also be obtained after a suitable tuning of parameters.
We consider Abelian M5 brane on a six-manifold which we take as a circle bundle over a five-manifold $M$. We compute the zero mode part of the M5 brane partition function using Chern-Simons theory and Hamiltonian formulation respectively and find an agreement. We also show that the D4 brane on $M$ shares exactly the same zero mode partition function again using the Hamiltonian formulation. For the oscillator modes we find that KK modes associated with the circle compactification are missing from the D4 brane. By making an infinitesimal noncommutative deformation we have instanton threshold bou…
We analyze three aspects of N=1 heterotic string compactifications on elliptically fibered Calabi-Yau threefolds: stability of vector bundles, five-brane instanton transitions and chiral matter. First we show that relative Fourier-Mukai transformation preserves absolute stability. This is relevant for vector bundles whose spectral cover is reducible. Then we derive an explicit formula for the number of moduli which occur in (vertical) five-brane instanton transitions provided a certain vanishing argument applies. Such transitions increase the holonomy of the heterotic vector bundle and cause g…
