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Michael B. Green

Publications and source records attributed to Michael B. Green.

At least 73 records · Page 4Linked to original sources
arXiv2000

D-instanton induced interactions on a D3-brane

Non-perturbative features of the derivative expansion of the effective action of a single D3-brane are obtained by considering scattering amplitudes of open and closed strings. This motivates expressions for the coupling constant dependence of world-volume interactions of the form $(\partial F)^4$ (where F is the Born-Infeld field strength), $(\partial^2ϕ)^4$ (where $ϕ$ are the normal coordinates of the D3-brane) and other interactions related by $\calN=4$ supersymmetry. These include terms that transform with non-trivial modular weight under Montonen-Olive duality. The leading D-instanton contributions that enter into these effective interactions are also shown to follow from an explicit stringy construction of the moduli space action for the D-instanton/D3-brane system in the presence of D3-brane open-string sources (but in the absence of a background antisymmetric tensor potential). Extending this action to include closed-string sources leads to a unified description of non-perturbative terms in the effective action of the form (embedding curvature)$^2$ together with open-string interactions that describe contributions of the second fundamental form.

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arXiv1999

D-instantons, Strings and M-theory

The R^4 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 R^4 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 R^4 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 R^4 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)}R^4. The generalization to compactification on T^3 as well as implications for non-renormalization theorems in D-string and D-particle interactions are briefly discussed.

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arXiv1999

Instantons and Non-renormalisation in AdS/CFT

The series of perturbative fluctuations around a multi-instanton contribution to a specific class of correlation functions of supercurrents in $\cal N=4$ supersymmetric SU(N) Yang-Mills theory is examined in the light of the AdS/CFT correspondence. Subject to certain plausible assumptions, we argue that a given term in the 1/N expansion in such a background receives only a finite number of perturbative corrections in the 't Hooft limit. Such instanton non-renormalisation theorems would explain, for example, the exact agreement of certain weak coupling Yang-Mills instanton calculations with the strong coupling predictions arising from D-instanton effects in string theory amplitudes. These non-renormalisation theorems essentially follow from the assumption of a well defined derivative $(α^{\prime})$ expansion in the string theory dual of the Yang-Mills theory.

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arXiv1999

The low energy expansion of the one-loop type II superstring amplitude

The one-loop four-graviton amplitude in either of the type II superstring theories is expanded in powers of the external momenta up to and including terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series are obtained by integrating powers of the two-dimensional scalar field theory propagator over the toroidal world-sheet as well as the moduli of the torus. The values of these coefficients match expectations based on duality relations between string theory and eleven-dimensional supergravity.

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arXiv1999

Light-cone Quantum Mechanics of the Eleven-dimensional Superparticle

The linearized interactions of eleven-dimensional supergravity are obtained in a manifestly supersymmetric light-cone gauge formalism. These vertices are used to calculate certain one-loop processes involving external gravitini, antisymmetric three-form potentials and gravitons, thereby determining some protected terms in the effective action of M-theory compactified on a two-torus.

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arXiv1999

An SL(2,Z) anomaly in IIB supergravity and its F-theory interpretation

The SL(2,Z) duality transformations of type IIB supergravity are shown to be anomalous in generic F-theory backgrounds due to the anomalous transformation of the phase of the chiral fermion determinant. The anomaly is partially cancelled provided the ten-dimensional type IIB theory lagrangian contains a term that is a ten-form made out of the composite U(1) field strength and four powers of the curvature. A residual anomaly remains uncancelled, and this implies a certain topological restriction on consistent backgrounds of the euclidean theory. A similar, but slightly stronger, restriction is also derived from an explicit F-theory compactification on K3 x M8 (where M8 is an eight-manifold with a nowhere vanishing chiral spinor) where the cancellation of tadpoles for Ramond--Ramond fields is only possible if M8 has an Euler character that is a positive multiple of 24. The interpretation of this restriction in the dual heterotic theory on T2 x M8 is also given.

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arXiv1999

Interconnections between type II superstrings, M theory and N=4 supersymmetric Yang--Mills

These lecture notes begin with a review of the first nonleading contributions to the derivative expansion of the M theory effective action compactified on a two-torus. The form of these higher-derivative interactions is shown to follow from ten-dimensional type IIB supersymmetry as well as from one-loop quantum corrections to classical eleven-dimensional supergravity. The detailed information concerning D-instanton effects encoded in these terms is related to the problem of evaluating the Witten index for $N$ D-particles in the type IIA theory. Using the AdS/CFT conjecture, it also leads to very specific predictions of multi-instanton contributions in $\cal N=4$ supersymmetric SU(N) Yang--Mills theory in the limit of strong 't Hooft coupling. [Extended version of lectures given at 22nd Johns Hopkins Workshop (Gothenberg, August 20-22 1998); `Quantum Aspects of Gauge Theories, Supersymmetry and Unification', TMR meeting (Corfu, September 20-26 1998); Andrjewski lectures (Berlin, November 1-6 1998).]

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arXiv1998

Supersymmetry Constraints on Type IIB Supergravity

Supersymmetry is used to derive conditions on higher derivative terms in the effective action of type IIB supergravity. Using these conditions, we are able to prove earlier conjectures that certain modular invariant interactions of order alpha' **3 relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z). We also discuss how these arguments generalize to terms of higher order in alpha', as well as to compactifications of supergravity.

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arXiv1998

Instantons in supersymmetric Yang-Mills and D-instantons in IIB superstring theory

The one-instanton contributions to various correlation functions of supercurrents in four-dimensional N=4 supersymmetric SU(2) Yang-Mills theory are evaluated to the lowest order in perturbation theory.Expressions of the same form are obtained from the leading effects of a single D-instanton extracted from the IIB superstring effective action around the AdS5*S5 background. This is in line with the suggested AdS/Yang-Mills correspondence. The relation between Yang--Mills instantons and D-instantons is further confirmed by the explicit form of the classical D-instanton solution in the AdS5*S5 background and its associated supermultiplet of zero modes. Speculations are made concerning instanton effects in the large-N_c limit of the SU(N_c) Yang-Mills theory.

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arXiv1998

Non-perturbative Effects in AdS5 * S5 String Theory and d=4 SUSY Yang-Mills

We show that five-dimensional anti de-Sitter space remains a solution to low-energy type IIB supergravity when the leading higher-derivative corrections to the classical supergravity (which are non-perturbative in the string coupling) are included. Furthermore, at this order in the low energy expansion of the IIB theory the graviton two-point and three-point functions in $AdS_5 \times S^5$ are shown not to be renormalized and a precise expression is obtained for the four-graviton and related S-matrix elements. By invoking Maldacena's conjectured connection between IIB superstring theory and supersymmetric Yang-Mills theory corresponding statements are obtained concerning correlation functions of the energy-momentum tensor and related operators in the large-N Yang-Mills theory. This leads to interesting non-perturbative statements and insights into the rôle of instantons in the gauge theory.

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arXiv1998

D-instanton partition functions

Duality arguments are used to determine D-instanton contributions to certain effective interaction terms of type II supergravity theories in various dimensions. This leads to exact expressions for the partition functions of the finite N D-instanton matrix model in d=4 and 6 dimensions that generalize our previous expression for the case d=10. These results are consistent with the fact that the Witten index of the T-dual D-particle process should only be non-vanishing for d=10.

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arXiv1998

(8,0) Quantum mechanics and symmetry enhancement in type I' superstrings

The low-energy supersymmetric quantum mechanics describing D-particles in the background of D8-branes and orientifold planes is analyzed in detail, including a careful discussion of Gauss' law and normal ordering of operators. This elucidates the mechanism that binds D-particles to an orientifold plane, in accordance with the predictions of heterotic/type I duality. The ocurrence of enhanced symmetries associated with massless bound states of a D-particle with one orientifold plane is illustrated by the enhancement of $SO(14) \times U(1)$ to $E_8$ and $SO(12)\times U(1)$ to $E_7$ at strong type I' coupling. Enhancement to higher-rank groups involves both orientifold planes. For example, the enhanced $E_8 \times E_8 \times SU(2)$ symmetry at the self-dual radius of the heterotic string is seen as the result of two D8-branes coinciding midway between the orientifold planes, while the enhanced $SU(18)$ symmetry results from the coincidence of all sixteen D8-branes and $SO(34)$ when they also coincide with an orientifold plane. As a separate by-product, the s-rule of brane-engineered gauge theories is derived by relating it through a chain of dualities to the Pauli exclusion principle.

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arXiv1997

Sixteen-fermion and related terms in M-theory on T**2

Certain one-loop processes in eleven-dimensional supergravity compactified on T**2 determine exact, non-perturbative, terms in the effective action of type II string theories compactified on a circle. One example is the modular invariant U(1)-violating interaction of sixteen complex spin-1/2 fermions of ten-dimensional type IIB theory. This term, together with the (curvature)**4 term, and many other terms of the same dimension are all explicitly related by supersymmetry.

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arXiv1997

Monstrous Heterotic Quantum Mechanics

A compactification of the heterotic string is considered which describes a particle propagating in the symmetric space M = SO(9,1;Z)\SO(9,1;R)/SO(9;R) in interaction with excited states whose dynamics is (1+1)-dimensional. The model appears to describe D-particle dynamics in type IIA string theory on M.

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arXiv1997

Connections between M-theory and superstrings

This article reviews the non-perturbative structure of certain higher derivative terms in the type II string theory effective action and their connection to one-loop effects in eleven-dimensional supergravity compactified on a torus. New material is also included that was not presented in the talks.

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arXiv1997

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 nonperturbative 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-wound 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.

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arXiv1997

Anomalous Creation of Branes

In certain circumstances when two branes pass through each other a third brane is produced stretching between them. We explain this phenomenon by the use of chains of dualities and the inflow of charge that is required for the absence of chiral gauge anomalies when pairs of D-branes intersect.

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