Instanton Corrections Research Articles

Simple Calculation of Instanton Corrections in MASSIVE N = 2 SU(3) SYM

We give an explicit derivation of the Picard–Fuchs equations for N = 2 supersymmetric SU(3) Yang–Mills theory with Nf < 6 massive hypermultiplets in the fundamental representation. We determine the instanton corrections to the prepotential in the weak coupling region using the relation between Tr <ϕ2> and the prepotential. This method can be generalized straightforwardly to other gauge groups.

Stationary solutions of N = 2 supergravity

We discuss general bosonic stationary configurations of N=2, D=4 supergravity coupled to vector multiplets. The requirement of unbroken supersymmetries imposes constraints on the holomorphic symplectic section of the underlying special K\"ahler manifold. The corresponding solutions of the field equations are completely determined by a set of harmonic functions. As examples we discuss rotating black holes, Taub-NUT and Eguchi-Hanson like instantons for the STU model. In addition, we discuss, in the static limit, worldsheet instanton corrections to the STU black hole solution, in the neighbourhood of a vanishing 4-cycle of the Calabi-Yau manifold. Our procedure is quite general and includes all known black hole solutions that can be embedded into N=2 supergravity.

D-instantons, strings and M-theory

The R4 terms in the effective action for M-theory compactified on a two-torus are motivated by combining one-loop results in type II superstring theories with the Sl(2, Z) duality symmetry. The conjectured expression reproduces precisely the tree-level and one-loop R4 terms in the effective action of the type II string theories compactified on a circle, together with the expected infinite sum of instanton corrections. This conjecture implies that the R4 terms in ten-dimensional string type II theories receive no perturbative corrections beyond one loop and there are also no non-perturbative corrections in the ten-dimensional IIA theory. Furthermore, the eleven-dimensional M-theory limit exists, in which there is an R4 term that originates entirely from the one-loop contribution in the type IIA theory and is related by supersymmetry to the eleven-form C(3) R4. The generalization to compactification on T3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.

Dynamics of N = 2 supersymmetric gauge theories in three dimensions

We study the structure of the moduli spaces of vacua and superpotentials of N = 2 supersymmetric gauge theories in three dimensions. By analyzing the instanton corrections, we compute the exact superpotentials and determine the quantum Coulomb and Higgs branches of the theories in the weak coupling regions. We find candidates for non-trivial N = 2 superconformal field theories at the singularities of the moduli spaces. The analysis is carried out explicitly for gauge groups U( N c ) and SU( N c ) with N f flavors. We show that the field theory results are in complete agreement with the intersecting branes picture. We also compute the exact superpotentials for arbitrary gauge groups and arbitrary matter content.

Effects of D-instantons

Scattering of fundamental states of type IIB supergravity and superstring theory is discussed at low orders in perturbation theory in the background of a D-instanton. The integration over fermionic zero-modes in both the low energy supergravity and in the string theory leads to explicit non-perturbative terms in the effective action. These include a single instanton correction to the known tree-level and one-loop R 4 interactions. The ‘spectrum’ of multiply charged D-instantons is deduced by T-duality in nine dimensions from multiply would world-lines of marginally bound D-particles. This, and other clues, lead to a conjectured SL(2, Z ) completion of the R 4 terms which suggests that they are not renormalized by perturbative corrections in the zero-instanton sector beyond one-loop. The string theory unit-charged D-instanton gives rise to point-like effects in fixed-angle scattering, raising unresolved issues concerning distance scales in superstring theory.

Can only flavor-nonsinglet H dibaryons be stable against strong decays?

Using the QCD sum-rule approach, we show that the flavor-nonsinglet H dibaryon states with J{sup {pi}}=1{sup +}, J{sup {pi}}=0{sup +}, I=1 (27 plet) are nearly degenerate with the J{sup {pi}}=0{sup +}, I=0 singlet H{sub 0} dibaryon, which has been predicted to be stable against strong decay, but has not been observed. Our calculation, which does not require an instanton correction, suggests that the H{sub 0} is slightly heavier than these flavor-nonsinglet H{close_quote}s over a wide range of the parameter space. If the singlet H{sub 0} mass lies above the {Lambda}{Lambda} threshold (2231 MeV), then the strong interaction breakup to {Lambda}{Lambda} would produce a very broad resonance in the {Lambda}{Lambda} invariant mass spectrum which would be very difficult to observe. On the other hand, if these flavor-nonsinglet J=0 and 1 H dibaryons are also above the {Lambda}{Lambda} threshold, but below the {Xi}{sup 0}n breakup threshold (2254 MeV), then because the direct, strong interaction decay to the {Lambda}{Lambda} channel is forbidden, these flavor-nonsinglet states might be more amenable to experimental observation. The present results allow a possible reconciliation between the reported observation of {Lambda}{Lambda} hypernuclei, which argue against a stable H{sub 0}, and the possible existence of H dibaryons in general. {copyright}more » {ital 1997} {ital The American Physical Society}« less

An analysis of soft terms in Calabi-Yau compactifications

We perform an analysis of the soft supersymmetry-breaking terms arising in Calabi-Yau compactifications. The sigma-model contribution and the instanton correction to the K\"ahler potential are included in the computation. The existence of off-diagonal moduli and matter metrics gives rise to specific features as the possibility of having scalars heavier than gauginos or the presence of tachyons. Although non-universal soft terms is a natural situation, we point out that there is an interesting limit where universality is achieved. Finally, we compare these results with those of orbifold compactifications. Although they are qualitatively similar some features indeed change. For example, sum rules found in orbifold models which imply that on average the scalars are lighter than gauginos can be violated in Calabi-Yau manifolds.

Subleading contributions from instanton corrections in N = 2 supersymmetric black hole entropy

We present subleading corrections to the N = 2 supersymmetric black hole entropy. These subleading contributions correspond to instanton corrections of the Type II string theory. In particular we consider an axion free black hole solution of low-energy effective Type II string theory. We present a procedure to include successiveall instanton corrections. Expanding these corrections at particular points in moduli space yields polynomial and logarithmic instanton corrections to the classical black hole entropy. We comment on a microscopic interpretation of these instanton corrections and find that the logarithmic corrections correspond to subleading terms in the degeneracy of the spectrum of an underlying quantum theory.

Mirror symmetry in three-dimensional gauge theories, [formula omitted] and D-brane moduli spaces

We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N = 4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2, Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane world-volume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping 5-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.

Isospin breaking and instantons in QCD nucleon sum rules

We study isospin breaking instanton corrections to the operator product expansion of the nucleon correlation functions. After a comparison with quark model calculations based on the 't Hooft interaction, we examine the role of instantons in the corresponding QCD sum rules. Instanton contributions are found to be absent in the chirally even sum rule, but significant in the chirally-odd one. They improve the consistency of both sum rules and favor a value of the isovector quark condensate close to the chiral estimate.

Prepotentials in N = 2 supersymmetric SU(3) YM theory with massless hypermultiplets

We explicitly determine the instanton corrections to the prepotential for N = 2 supersymmetric SU(3) Yang-Mills theory with massless hypermultiplets in the weak coupling regions u → ∞ and u a ̊ ∞ . We construct the Picard-Fuchs equations for N f < 6 and calculate the monodromies using Picard-Lefschetz theorem for N f = 2, 4. For all N f < 6 the instanton corrections to the prepotential are determined using the relation between Tr( Φ 2) and the prepotential.

Prepotential of N=2 SU(2) Yang–Mills gauge theory coupled with a massive matter multiplet

We discuss the N=2 SU(2) Yang–Mills theory coupled with a massive matter in the weak coupling. In particular, we obtain the instanton expansion of its prepotential. Instanton contributions in the mass-less limit are completely reproduced. We study also the double scaling limit of this massive theory and find that the prepotential with instanton corrections in the double scaling limit coincides with that of N=2 SU(2) Yang–Mills theory without matter.

D-branes on Calabi-Yau spaces and their mirrors

We study the boundary states of D-branes wrapped around supersymmetric cycles in a general Calabi-Yau manifold. In particular, we show how the geometric data on the cycles are encoded in the boundary states. As an application, we analyze how the mirror symmetry transforms D-branes, and we verify that it is consistent with the conjectured periodicity and the monodromy of the Ramond-Ramond field configuration on a Calabi-Yau manifold. This also enables us to study open string worldsheet instanton corrections and relate them to closed string instanton counting. The cases when the mirror symmetry is realized as T-duality are also discussed.

NONPERTURBATIVE EFFECTIVE ACTIONS OF (N=2)-SUPERSYMMETRIC GAUGE THEORIES

We elaborate on our previous work on (N=2)-supersymmetric Yang-Mills theory. In particular, we show how to explicitly determine the low energy quantum effective action for G=SU(3) from the underlying hyperelliptic Riemann surface, and calculate the leading instanton corrections. This is done by solving Picard-Fuchs equations and asymptotically evaluating period integrals. We find that the dynamics of the SU(3) theory is governed by an Appell system of type F4, and compute the exact quantum gauge coupling explicitly in terms of Appell functions.

On the quantum moduli space of vacua of N = 2 supersymmetric gauge theories

Families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SO( N c ) gauge theories coupled to N f flavors of quarks in the vector representation are constructed. The quantum moduli spaces for 2 N f < N c − 1 are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue calculations. The quantum moduli spaces for 2 N f ⩾ N c − 1 theories are parameterized and their general structure is worked out using residue calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. The results presented here together with recent results of Martinec and Warner provide a natural conjecture for the form of the curves for the other gauge groups.

A Two Parameter Family of the Calabi–Yaud-Fold

We study a two parameter family of Calabi–Yaud-fold by means of mirror symmetry. We construct mirror maps and calculate correlation functions associated with Kähler moduli in the original manifold. We find there are more complicated instanton corrections of these couplings than threefolds, which is expected to reflect families of instantons with continuous parameters.

Prepotentials in N = 2 SU(2) supersymmetric Yang-Mills theory with massless hypermultiplets

We calculate the prepotential of the low-energy effective action for N = 2 SU(2) supersymmetric Yang-Mills theory with N f massless hypermultiplets ( N f = 1, 2, 3). The precise evaluation of the instanton corrections is performed by making use of the Picard-Fuchs equations associated with elliptic curves. The flavor dependence of the instanton effect is determined explicitly both in the weak- and strong-coupling regimes.

Fivebranes, membranes and non-perturbative string theory

Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order e −1/ g s contributions, where g s is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the Calabi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the Kähler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odd-dimensional cycles in the Calabi-Yau space to a sum in the IIB theory over supersymmetric, even-dimensional cycles in the mirror.

On the instanton contributions to the masses and couplings of E6 singlets

We consider the gauge neutral matter in the low-energy effective action for string theory compactification on a Calabi-Yau manifold with (2,2) world-sheet supersymmetry. At the classical level these states (the 1's of E 6) correspond to the cohomology group H 1( M , End T). We examine the first order contribution of instantons to the mass matrix of these particles. In principle, these corrections depend on the Kähler parameters t i through factors of the form e 2 πit i and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold P 4[5]. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however non-zero and the contribution of a given instanton may develop poles associated with instantons coalescing for certain values of the complex structure. This can happen when the underlying Calabi-Yau manifold is smooth. Hence these poles must cancel between the coalescing instantons in order that the superpotential be finite. We examine also the Yukawa couplings involving neutral matter 1 3 and neutral and charged fields 27 · 27 · 1 , which have been little investigated even though they are of phenomenological interest. We study the general conditions under which these couplings vanish classically. We also calculate the first-order world-sheet instanton correction to these couplings and argue that these also vanish.

On the quantum moduli space of vacua of N = 2 supersymmetric SU( Nc) gauge theories

We construct families of hyper-elliptic curves which describe the quantum moduli spaces of vacua of N = 2 supersymmetric SU( N c ) gauge theories coupled to N f flavors of quarks in the fundamental representation. The quantum moduli spaces for N f < N c are determined completely by imposing R-symmetry, instanton corrections and the proper classical singularity structure. These curves are verified by residue and weak coupling monodromy calculations. The quantum moduli spaces for N f ⩾ N c theories are parameterized and their general structure is worked out using residue calculations. Global symmetry considerations suggest a complete description of them. The results are supported by weak coupling monodromy calculations. The exact metrics on the quantum moduli spaces as well as the exact spectrum of stable massive states are derived. We find an example of a novel symmetry of a quantum moduli space: Invariance under the exchange of a moduli parameter and the bare mass. We apply our method for the construction of the quantum moduli spaces of vacua of N = 1 supersymmetric theories in the Coulomb phase.