arXiv subjects

E. D'Hoker

Publications and source records attributed to E. D'Hoker.

12 recordsLinked to original sources

arXiv2003

Systematics of Quarter BPS operators in N=4 SYM

A systematic construction is presented of 1/4 BPS operators in N=4 superconformal Yang-Mills theory, using either analytic superspace methods or components. In the construction, the operators of the classical theory annihilated by 4 out of 16 supercharges are arranged into two types. The first type consists of those operators that contain 1/4 BPS operators in the full quantum theory. The second type consists of descendants of operators in long unprotected multiplets which develop anomalous dimensions in the quantum theory. The 1/4 BPS operators of the quantum theory are defined to be orthogonal to all the descendant operators with the same classical quantum numbers. It is shown, to order $g^2$, that these 1/4 BPS operators have protected dimensions.

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arXiv2000

Near-Extremal Correlators and Generalized Consistent Truncation for AdS_{4|7}\times S^{7|4}

We present conjectures for the space-time form and leading large N dependence of extremal and near-extremal correlation functions in the \N=8 superconformal Yang-Mills theory in d=3 as well as in the (0,2) superconformal theory in d=6, using their gravity duals with M-theory on $AdS_4\times §^7$ and $AdS_7 \times §^4$ respectively. As a key part of the conjectures, we argue that the bulk couplings associated with extremal and near-extremal field configurations in the corresponding $AdS_4$ and $AdS_7$ gauged supergravities vanish. The vanishing of these couplings constitutes a generalization of the property of consistent truncation of the Kaluza-Klein modes.

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arXiv2000

Near-extremal correlators and vanishing supergravity couplings in AdS/CFT

We study near-extremal n-point correlation functions of chiral primary operators, in which the maximal scale dimension k is related to the others by k=\sum_i k_i-m with m equal to or smaller than n-3. Through order g^2 in field theory, we show that these correlators are simple sums of terms each of which factors into products of lower-point correlators. Terms which contain only factors of two- and three-point functions are not renormalized, but other terms have non-vanishing order g^2 corrections. We then show that the contributing AdS exchange diagrams neatly match this factored structure. In particular, for n=4,5 precise agreement in form and coefficient is established between supergravity and the non-renormalized factored terms from field theory. On the other hand, contact diagrams in supergravity would produce a non-factored structure. This leads us to conjecture that the corresponding bulk couplings vanish, so as to achieve full agreement between the structure of these correlators in supergravity and weak-coupling field theory.

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arXiv1999

Instanton Recursion Relations for the Effective Prepotential in N=2 Super Yang-Mills

Linear recursion relations for the instanton corrections to the effective prepotential of N=2 supersymmetric gauge theories with an arbitrary number of hypermultiplets in the fundamental representation of an arbitrary classical gauge group are dervied. The construction proceeds from the Seiberg-Witten solutions and the renormalization group type equations for the prepotential. Successive iterations of these recursion relations allow us to simple obtain instanton corrections to arbitrarily high order, which we exhibit explicitly up to 6-th order. For gauge groups SU(2) and SU(3), our results agree with previous ones.

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arXiv1999

Extremal Correlators in the AdS/CFT Correspondence

The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t ϕϕ$ and $s ϕϕ$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 \times S^5$.

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arXiv1999

Lax Pairs and Spectral Curves for Calogero-Moser and Spin Calogero-Moser Systems

We summarize recent results on the construction of Lax pairs with spectral parameter for the twisted and untwisted elliptic Calogero-Moser systems associated with arbitrary simple Lie algebras, their scaling limits to Toda systems, and their role in Seiberg-Witten theory. We extend part of this work by presenting a new parametrization for the spectral curves for elliptic spin Calogero-Moser systems associated with SL(N).

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arXiv1999

Seiberg-Witten Theory and Integrable Systems

We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. The first deals with the resolution of the non-perturbative low energy dynamics of certain N=2 supersymmetric Yang-Mills theories. We concentrate on the theories with one massive hypermultiplet in the adjoint representation of an arbitrary gauge algebra G. The second deals with the construction of Lax pairs with spectral parameter for certain classical mechanics Calogero-Moser integrable systems associated with an arbitrary Lie algebra G. We review the solution to both of these problems as well as their interrelation.

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arXiv1998

Order Parameters, Free Fermions, and Conservation Laws for Calogero-Moser Systems

The classical order parameters for the $\N=2$ supersymmetric SU(N) gauge theory with matter in the adjoint representation are exhibited explicitly as conservation laws for the elliptic Calogero-Moser system. Central to the construction are certain elliptic function identities, which arise from considering Feynman diagrams in a theory of free fermions with twisted boundary conditions.

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arXiv1998

Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for General Lie Algebras

The Seiberg-Witten curves and differentials for $\N=2$ supersymmetric Yang-Mills theories with one hypermultiplet of mass $m$ in the adjoint representation of the gauge algebra $\G$, are constructed for arbitrary classical or exceptional $\G$ (except $G_2$). The curves are obtained from the recently established Lax pairs with spectral parameter for the (twisted) elliptic Calogero-Moser integrable systems associated with the algebra $\G$. Curves and differentials are shown to have the proper group theoretic and complex analytic structure, and to behave as expected when $m$ tends either to 0 or to $\infty$. By way of example, the prepotential for $\G = D_n$, evaluated with these techniques, is shown to agree with standard perturbative results. A renormalization group type equation relating the prepotential to the Calogero-Moser Hamiltonian is obtained for arbitrary $\G$, generalizing a previous result for $\G = SU(N)$. Duality properties and decoupling to theories with other representations are briefly discussed.

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arXiv1998

Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras

We construct a Lax pair with spectral parameter for the elliptic Calogero-Moser Hamiltonian systems associated with each of the finite dimensional Lie algebras, of the classical and of the exceptional type. When the spectral parameter equals one of the three half periods of the elliptic curve, our result for the classical Lie algebras reduces to one of the Lax pairs without spectral parameter that were known previously. These Calogero-Moser systems are invariant under the Weyl group of the associated untwisted affine Lie algebra. For non-simply laced Lie algebras, we introduce new integrable systems, naturally associated with twisted affine Lie algebras, and construct their Lax operators with spectral parameter (except in the case of $G_2$).

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arXiv1998

Calogero-Moser and Toda Systems for Twisted and Untwisted Affine Lie Algebras

The elliptic Calogero-Moser Hamiltonian and Lax pair associated with a general simple Lie algebra $\G$ are shown to scale to the (affine) Toda Hamiltonian and Lax pair. The limit consists in taking the elliptic modulus $τ$ and the Calogero-Moser couplings $m$ to infinity, while keeping fixed the combination $M = m e^{i πδτ}$ for some exponent $δ$. Critical scaling limits arise when $1/δ$ equals the Coxeter number or the dual Coxeter number for the untwisted and twisted Calogero-Moser systems respectively; the limit consists then of the Toda system for the affine Lie algebras $\G^{(1)}$ and $(\G ^{(1)})^\vee$. The limits of the untwisted or twisted Calogero-Moser system, for $δ$ less than these critical values, but non-zero, consists of the ordinary Toda system, while for $δ=0$, it consists of the trigonometric Calogero-Moser systems for the algebras $\G$ and $\G^\vee$ respectively.

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arXiv1994

The Box Graph In Superstring Theory

In theories of closed oriented superstrings, the one loop amplitude is given by a single diagram, with the topology of a torus. Its interpretation had remained obscure, because it was formally real, converged only for purely imaginary values of the Mandelstam variables, and had to account for the singularities of both the box graph and the one particle reducible graphs in field theories. We present in detail an analytic continuation method which resolves all these difficulties. It is based on a reduction to certain minimal amplitudes which can themselves be expressed in terms of double and single dispersion relations, with explicit spectral densities. The minimal amplitudes correspond formally to an infinite superposition of box graphs on $ϕ^3$ like field theories, whose divergence is responsible for the poles in the string amplitudes. This paper is a considerable simplification and generalization of our earlier proposal published in Phys. Rev. Lett. 70 (1993) p 3692.

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