On Low-Energy Effective Actions in N = 2, 4 Superconformal Theories in Four Dimensions

We study some aspects of low-energy effective actions in 4-d superconformal gauge theories on the Coulomb branch. We describe superconformal invariants constructed in terms of N=2 abelian vector multiplet which play the role of building blocks for the N=2,4 supersymmetric low-energy effective actions. We compute the one-loop effective actions in constant N=2 field strength background in N=4 SYM theory and in N=2 SU(2) SYM theory with four hypermultiplets in fundamental representation. Using the classification of superconformal invariants we then find the manifestly N=2 superconformal form of these effective actions. While our explicit computations are done in the one-loop approximation, our conclusions about the structure of the effective actions in N=2 superconformal theories are general. We comment on some applications to supergravity - gauge theory duality in the description of D-brane interactions.Comment: 18 pages, latex, comments/reference adde

Higher-Derivative Terms in N=2 Supersymmetric Effective Actions

We show how to systematically construct higher-derivative terms in effective actions in harmonic superspace despite the infinite redundancy in their description due to the infinite number of auxiliary fields. Making an assumption about the absence of certain superspace Chern-Simons-like terms involving vector multiplets, we write all 3- and 4-derivative terms on Higgs, Coulomb, and mixed branches. Among these terms are several with only holomorphic dependence on fields, and at least one satisfies a non-renormalization theorem. These holomorphic terms include a novel 3-derivative term on mixed branches given as an integral over 3/4 of superspace. As an illustration of our method, we search for Wess-Zumino terms in the low energy effective action of N=2 supersymmetric QCD. We show that such terms occur only on mixed branches. We also present an argument showing that the combination of space-time locality with supersymmetry implies locality in the anticommuting superspace coordinates of for unconstrained superfields.Comment: 30 pages. Added references and simplified final form of WZ ter

Complete N=4 Structure of Low-Energy Effective Action in N=4 Super Yang-Mills Theories

Using the ${\cal N}=2$ superfield approach, we construct full ${\cal N}=4$ supersymmetric low-energy effective actions for ${\cal N}=4$ SYM models, with both ${\cal N}=2$ gauge superfield strengths and hypermultiplet superfields included. The basic idea is to complete the known non-holomorphic effective potentials which depend only on ${\cal N}=2$ superfield strengths $W$ and ${\bar W}$ to the full on-shell ${\cal N}=4$ invariants by adding the appropriate superfield hypermultiplet terms. We prove that the effective potentials of the form ${ln} W {ln} \bar W$ can be ${\cal N} = 4$ completed in this way and present the precise structure of the corresponding completions. However, the effective potentials of the non-logarithmic form suggested in hep-th/9811017 and hep-th/9909020 do not admit the ${\cal N}=4$ completion. Therefore, such potentials cannot come out as (perturbative or non-perturbative) quantum corrections in ${\cal N}=4$ SYM models.Comment: 14 pages, Latex, no figures, slight corrections, refs adde

Complete Low-Energy Effective action in N=4 SYM: a Direct N=2 Supergraph Calculation

Using the covariant N=2 harmonic supergraph techniques we calculate the one-loop low-energy effective action of N=4 super-Yang-Mills theory in Coulomb branch with gauge group SU(2) spontaneously broken down to U(1). The full dependence of the low-energy effective action on both the hypermultiplet and gauge fields is determined. The direct quantum calculation confirms the correctness of the exact N=4 SYM low-energy effective action derived in hep-th/0111062 on the purely algebraic ground by invoking a hidden N=2 supersymmetry which completes the manifest N=2 one to N=4. Our results provide an exhaustive solution to the problem of finding out the exact completely N=4 supersymmetric low-energy effective action for the theory under consideration.Comment: LaTeX, 21 pages; minor correction

Scale Invariant Low-Energy Effective Action in N=3 SYM Theory

Using the harmonic superspace approach we study the problem of low-energy effective action in N=3 SYM theory. The candidate effective action is a scale and \gamma_5-invariant functional in full N=3 superspace built out of N=3 off-shell superfield strengths. This action is constructed as N=3 superfield generalization of F^4/\phi^4 component term which is leading in the low-energy effective action and is simultaneously the first nontrivial term in scale invariant Born-Infeld action. All higher-order terms in the scale invariant Born-Infeld action are also shown to admit an off-shell superfield completion in N=3 harmonic superspace.Comment: 17 pages; v2: typos correcte

Confinement, the gluon propagator and the interquark potential for heavy mesons

The interquark static potential for heavy mesons described by a massive One Gluon Exchange interaction obtained from the propagator of the truncated Dyson-Schwinger equations does not reproduced the expected Cornell potential. I show that no formulation based on a finite propagator will lead to confinement of quenched QCD. I propose a mechanism based on a singular nonperturbative coupling constant which has the virtue of giving rise to a finite gluon propagator and (almost) linear confinement. The mechanism can be slightly modified to produce the screened potentials of unquenched QCD.Comment: 12 pages and 7 figure

New massive supergravity multiplets

We present new off-shell formulations for the massive superspin-3/2 multiplet. In the massless limit, they reduce respectively to the old minimal (n=-1/3) and non-minimal ($n\neq -1/3, 0$) linearized formulations for 4D N=1 supergravity. Duality transformations, which relate the models constructed, are derived.Comment: 18 pages, LaTeX; v2: minor changes, references adde

Two-loop N=4 Super Yang Mills effective action and interaction between D3-branes

We compute the leading low-energy term in the planar part of the 2-loop contribution to the effective action of $\N=4$ SYM theory in 4 dimensions, assuming that the gauge group $SU(N+1)$ is broken to $SU(N) x U(1)$ by a constant scalar background $X$. While the leading 1-loop correction is the familiar $c_1 F^4/|X|^4$ term, the 2-loop expression starts with $c_2 F^6/|X|^8$. The 1-loop constant $c_1$ is known to be equal to the coefficient of the $F^4$ term in the Born-Infeld action for a probe D3-brane separated by distance $|X|$ from a large number $N$ of coincident D3-branes. We show that the same is true also for the 2-loop constant $c_2$: it matches the coefficient of the $F^6$ term in the D3-brane probe action. In the context of the AdS/CFT correspondence, this agreement suggests a non-renormalization of the coefficient of the $F^6$ term beyond two loops. Thus the result of hep-th/9706072 about the agreement between the $v^6$ term in the D0-brane supergravity interaction potential and the corresponding 2-loop term in the 1+0 dimensional reduction of $\N=4$ SYM theory has indeed a direct generalization to 1+3 dimensions, as conjectured earlier in hep-th/9709087. We also discuss the issue of gauge theory -- supergravity correspondence for higher order ($F^8$, etc.) terms.Comment: 33 pages, late

Vector-multiplet effective action in the non-anticommutative charged hypermultiplet model

We investigate the quantum aspects of a charged hypermultiplet in deformed N=(1,1) superspace with singlet non-anticommutative deformation of supersymmetry. This model is a "star" modification of the hypermultiplet interacting with a background Abelian vector superfield. We prove that this model is renormalizable in the sense that the divergent part of the effective action is proportional to the N=(1,0) non-anticommutative super Yang-Mills action. We also calculate the finite part of the low-energy effective action depending on the vector multiplet, which corresponds to the (anti)holomorphic potential. The holomorphic piece is just deformed to the star-generalization of the standard holomorphic potential, while the antiholomorphic piece is not. We also reveal the component structure and find the deformation of the mass and the central charge.Comment: 22 pages, 1 figur

Superfield theory and supermatrix model

We study the noncommutative superspace of arbitrary dimensions in a systematic way. Superfield theories on a noncommutative superspace can be formulated in two folds, through the star product formalism and in terms of the supermatrices. We elaborate the duality between them by constructing the isomorphism explicitly and relating the superspace integrations of the star product Lagrangian or the superpotential to the traces of the supermatrices. We show there exists an interesting fine tuned commutative limit where the duality can be still maintained. Namely on the commutative superspace too, there exists a supermatrix model description for the superfield theory. We interpret the result in the context of the wave particle duality. The dual particles for the superfields in even and odd spacetime dimensions are D-instantons and D0-branes respectively to be consistent with the T-duality.Comment: 1+16 pages, no figure; expanded version, references added; Convention for Clifford algebra improve