Non-renormalization Theorem Research Articles

Higher derivative operators from Scherk-Schwarz supersymmetry breaking on Script T2/Z2.

In orbifold compactifications on T^2/Z_2 with Scherk-Schwarz supersymmetry breaking, it is shown that (brane-localised) superpotential interactions and (bulk) gauge interactions generate at one-loop higher derivative counterterms to the mass of the brane (or zero-mode of the bulk) scalar field. These brane-localised operators are generated by integrating out the bulk modes of the initial theory which, although supersymmetric, is nevertheless non-renormalisable. It is argued that such operators, of non-perturbative origin and not protected by non-renormalisation theorems, are generic in orbifold compactifications and play a crucial role in the UV behaviour of the two-point Green function of the scalar field self-energy. Their presence in the action with unknown coefficients prevents one from making predictions about physics at (momentum) scales close to/above the compactification scale(s). Our results extend to the case of two dimensional orbifolds, previous findings for S^1/Z_2 and S^1/(Z_2 x Z_2') compactifications where brane-localised higher derivative operators are also dynamically generated at loop level, regardless of the details of the supersymmetry breaking mechanism. We stress the importance of these operators for the hierarchy and the cosmological constant problems in compactified theories.

Effective action ofβ-deformedN=4SYM theory and AdS/CFT

We compute the one-loop effective action in $\mathcal{N}=1$ superconformal $SU(N)$ gauge theory which is an exactly marginal deformation of the $\mathcal{N}=4$ SYM. We consider an Abelian background of constant $\mathcal{N}=1$ gauge field and single chiral scalar. While for finite $N$ the effective action depends nontrivially on the deformation parameter $q={e}^{i\ensuremath{\pi}\ensuremath{\beta}}$, this dependence disappears in the large $N$ limit if the parameter $\ensuremath{\beta}$ is real. This conclusion matches the strong-coupling prediction coming from the form of a D3-brane probe action in the dual supergravity background: for the simplest choice of the D3-brane position the probe action happens to be the same as for a D3-brane in $Ad{S}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ placed parallel to the boundary of $Ad{S}_{5}$. This suggests that in the real $\ensuremath{\beta}$ deformation case there exists a large $N$ nonrenormalization theorem for the ${F}^{4}$ term in the action.

R-symmetry in the Q-exact [formula omitted] 2d lattice Wess–Zumino model

In this article we explore the R-symmetry of the ( 2 , 2 ) 2d Wess–Zumino model. We study whether or not this symmetry is approximately realized in the Q-exact lattice version of this theory. Our study is nonperturbative: it relies on Monte Carlo simulations with dynamical fermions. Irrelevant operators in the lattice action explicitly break the R-symmetry. In spite of this, it is found to be a symmetry of the effective potential. We find nonperturbative evidence that the nonrenormalization theorem of the continuum theory is recovered in the continuum limit; e.g., there is no additive mass renormalization. In our simulations we find that Fourier acceleration of the hybrid Monte Carlo algorithm allows us to avoid difficulties with critical slowing-down.

LESS IS MORE: NONRENORMALIZATION THEOREMS FROM LOWER DIMENSIONAL SUPERSPACE

We discuss a new class of non-renormalization theorems in [Formula: see text] and [Formula: see text] Super-Yang-Mills theory, obtained by using a superspace which makes a lower dimensional subgroup of the full supersymmetry manifest. Certain Wilson loops (and Wilson lines) belong to the chiral ring of the lower dimensional supersymmetry algebra, and their expectation values can be computed exactly.

One-loop Yukawas on intersecting branes

We calculate Yukawa interactions at one-loop on intersecting D6 branes. We demonstrate the non-renormalization theorem in supersymmetric configurations, and show how Yukawa beta functions may be extracted. In addition to the usual logarithmic running, we find the power-law dependence on the infra-red cut-off associated with Kaluza-Klein modes. Our results may also be used to evaluate coupling renormalization in non-supersymmetric cases.

Two-loop superstrings VI Nonrenormalization theorems and the 4-point function

The N-point amplitudes for the type II and heterotic superstrings at two-loop order and for N ⩽ 4 massless NS bosons are evaluated explicitly from first principles, using the method of projection onto superperiod matrices introduced and developed in the first five papers of this series. The gauge-dependent corrections to the vertex operators, identified in paper V, are carefully taken into account, and the crucial counterterms which are Dolbeault exact in one insertion point and de Rham closed in the remaining points are constructed explicitly. This procedure maintains gauge slice independence at every stage of the evaluation. Analysis of the resulting amplitudes demonstrates, from first principles, that for N ⩽ 3 , no two-loop corrections occur, while for N = 4 , no two-loop corrections to the low energy effective action occur for R 4 terms in the type II superstrings, and for F 4 , F 2 F 2 , F 2 R 2 , and R 4 terms in the heterotic strings.

A local formulation of lattice Wess-Zumino model with exact U(1)Rsymmetry

A lattice Wess-Zumino model is formulated on the basis of Ginsparg-Wilson fermions. In perturbation theory, our formulation is equivalent to the formulation by Fujikawa and Ishibashi and by Fujikawa. Our formulation is, however, free from a singular nature of the latter formulation due to an additional auxiliary chiral supermultiplet on a lattice. The model posssesses an exact U(1)R symmetry as a supersymmetric counterpart of the L?scher lattice chiral U(1) symmetry. A restration of the supersymmetric Ward-Takahashi identity in the continuum limit is analyzed in renormalized perturbation theory. In the one-loop level, a supersymmetric continuum limit is ensured by suitably adjusting a coefficient of a single local term *. The non-renormalization theorem holds to this order of perturbation theory. In higher orders, on the other hand, coefficents of local terms with dimension ? 4 that are consistent with the U(1)R symmetry have to be adjusted for a supersymmetric continuum limit. The origin of this complexicity in higher-order loops is clarified on the basis of the Reisz power counting theorem. Therefore, from a view point of supersymmetry, the present formulation is not quite better than a lattice Wess-Zumino model formulated by using Wilson fermions, although a number of coefficients which require adjustment is much less due to the exact U(1)R symmetry. We also comment on an exact non-linear fermionic symmetry which corresponds to the one studied by Bonini and Feo; an existence of this exact symmetry itself does not imply a restoration of supersymmetry in the continuum limit without any adjustment of parameters.

M-Theory Phenomenology and See-Saw Mechanisms

A version of M-theory phenomenology is proposed in which the symmetry is based on the group $SO(10) \times SO(10) \times SO(10) \times U(1) \times U(1)$. Each SO(10) group acts on a single generation. The $U(1) \times U(1)$ is regarded as the hidden sector symmetry group. The supersymmetry is broken in the hidden sector by the Fayet-Iliopoulos $D$-term for each group. The $D$-term is needed also to circumvent the powerful non-renormalization theorem since the $SO(10) \times SO(10) \times SO(10)$ is broken down to the usual SO(10) by the pair condensation of certain messenger sector multiplets. The exchange of U(1) gauge bosons gives an attractive force for the pair to be created and condensed. The off-diagonal mass matrix elements among the generations in these messenger sector multiplets are the source of the flavor dynamics including the CP violation. The pair condensation of another multiplet in the messenger sector leads to the doublet-triplet splitting. The SO(10) decuplet Higgs couples only to one of the generations. The other couplings should, therefore, be calculated as higher order corrections. We present our preliminary results on the calculation of the mass matrices and the mixing angles for leptons and quarks in this model.

Background field calculations and nonrenormalization theorems in 4d supersymmetric gauge theories and their low-dimensional descendants

We analyze the structure of multiloop supergraphs contributing to the effective Lagrangians in 4d supersymmetric gauge theories and in the models obtained from them by dimensional reduction. When d = 4 , this gives the renormalization of the effective charge. For d < 4 , the low-energy effective Lagrangian describes the metric on the moduli space of classical vacua. These two problems turn out to be closely related. In particular, we establish the relationship between the 4d nonrenormalization theorems (in minimal and extended supersymmetric theories) and their low-dimensional counterparts.

Matrix Models, Monopoles and Modified Moduli

Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We demonstrate via the matrix model solutions a relation between vacua of theories with different numbers of colors and flavors. This relation is due to an N=2 nonrenormalization theorem which is inherited by these N=1 theories. Specializing to the case Nf=Nc, the simplest theory containing baryons, we demonstrate that the explicit matrix model predictions for the locations on the Coulomb branch at which monopoles condense are consistent with the quantum modified constraints on the moduli in the theory. The matrix model solutions include the case that baryons obtain vacuum expectation values. In specific cases we check explicitly that these results are also consistent with the factorization of corresponding Seiberg-Witten curves. Certain results are easily understood in terms of M5-brane constructions of these gauge theories.

Non-renormalization for planar Wess–Zumino model

Using a non-perturbative functional method, where the quantum fluctuations are gradually set up, it is shown that the interaction of a N=1 Wess–Zumino model in 2+1 dimensions does not get renormalized. This result is valid in the framework of the gradient expansion and aims at compensating the lack of non-renormalization theorems.

Non-renormalization theorem originating in a new fixed point of the vector manifestation

We study the pion velocity at the critical temperature of chiral symmetry restoration in QCD. Starting from the premise that the bare effective field theory is to be defined from the underlying QCD, we incorporate the effects of Lorentz non-invariance into the bare theory by matching an effective field theory to QCD at a suitable matching scale, and investigate how the Lorentz non-invariance existing in the bare theory influences physical quantities. Using the hidden local symmetry model as the effective field theory, where the chiral symmetry restoration is realized as the vector manifestation (VM), we find that the pion velocity at the critical temperature receives neither quantum nor (thermal) hadronic corrections at the critical temperature even when we start from the bare theory with Lorentz symmetry breaking. This is likely the manifestation of a new fixed point in the Lorentz non-invariant formulation of the VM.

New nonrenormalization theorems for anomalous three point functions

Nonrenormalization theorems involving the transverse, i.e. non anomalous, part of the <VVA> correlator in perturbative QCD are proven. Some of their consequences and questions they raise are discussed.

On the two-loop four-derivative quantum corrections in 4D [formula omitted] superconformal field theories

In N=2,4 superconformal field theories in four space–time dimensions, the quantum corrections with four derivatives are believed to be severely constrained by non-renormalization theorems. The strongest of these is the conjecture formulated by Dine and Seiberg in hep-th/9705057 that such terms are generated only at one loop. In this note, using the background field formulation in N=1 superspace, we test the Dine–Seiberg proposal by comparing the two-loop F 4 quantum corrections in two different superconformal theories with the same gauge group SU( N): (i) N=4 SYM (i.e., N=2 SYM with a single adjoint hypermultiplet); (ii) N=2 SYM with 2 N hypermultiplets in the fundamental. According to the Dine–Seiberg conjecture, these theories should yield identical two-loop F 4 contributions from all the supergraphs involving quantum hypermultiplets, since the pure N=2 SYM and ghost sectors are identical provided the same gauge conditions are chosen. We explicitly evaluate the relevant two-loop supergraphs and observe that the F 4 corrections generated have different large N behaviour in the two theories under consideration. Our results are in conflict with the Dine–Seiberg conjecture.

On the relation between effective supersymmetric actions in different dimensions

We make two remarks: (i) Renormalization of the effective charge in a four-dimensional (supersymmetric) gauge theory is determined by the same graphs and is rigidly connected to the renormalization of the metric on the moduli space of the classical vacua of the corresponding reduced quantum-mechanical system. Supersymmetry provides constraints for possible modifications of the metric, and this gives us a simple proof of nonrenormalization theorems for the original four-dimensional theory. (ii) We establish a nontrivial relationship between the effective (0 + 1)-dimensional and (1 + 1)-dimensional Lagrangians. (The latter represent conventional Kählerian σ models.)

Intersecting D3-branes and holography

We study a defect conformal field theory describing D3-branes intersecting over two space-time dimensions. This theory admits an exact Lagrangian description which includes both two- and four-dimensional degrees of freedom, has $(4,4)$ supersymmetry and is invariant under global conformal transformations. Both two- and four-dimensional contributions to the action are conveniently obtained in a two-dimensional $(2,2)$ superspace. In a suitable limit, the theory has a dual description in terms of a probe D3-brane wrapping an ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{1}$ slice of ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{5}.$ We consider the AdS/CFT dictionary for this setup. In particular we find classical probe fluctuations corresponding to the holomorphic curve $wy=c{\ensuremath{\alpha}}^{\ensuremath{'}}.$ These fluctuations are dual to defect fields containing massless two-dimensional scalars which parametrize the classical Higgs branch, but do not correspond to states in the Hilbert space of the CFT. We also identify probe fluctuations which are dual to BPS superconformal primary operators and to their descendants. A nonrenormalization theorem is conjectured for the correlators of these operators, and verified to order ${g}^{2}.$

Perturbative and nonperturbative renormalization of anomalous quark triangles

Anomalous quark triangles with one axial and two vector currents are studied in special kinematics when one of the vector currents carries a soft momentum. According to the Adler–Bardeen theorem the anomalous longitudinal part of the triangle is not renormalized in the chiral limit. We derive a new nonrenormalization theorem for the transversal part of the triangle. This nonrenormalization, in difference with the longitudinal part, holds on only perturbatively. At the nonperturbative level we use the operator product expansion and the pion dominance in the longitudinal part to determine the magnetic susceptibility of the quark condensate, χ=−Nc/(4π2Fπ2).

Higher-derivative terms inN= 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.

Two-graviton interaction in pp-wave background in Matrix theory and Supergravity

We compute the two-body one-loop effective action for the Matrix theory in the pp-wave background, and compare it to the effective action on the Supergravity side in the same background. Agreement is found for the effective actions on both sides. This points to the existence of a supersymmetric nonrenormalization theorem in the pp-wave background.

Two-loop superstrings in hyperelliptic language II: the cosmological constant and the non-renormalization theorem

The vanishing of the cosmological constant and the non-renormalization theorem are verified at two loops by explicit computation using the hyperelliptic language and the newly obtained chiral measure of D'Hoker and Phong. A set of identities is found which is used in the verification of the non-renormalization theorem and leads to a great simplification of the calculation of the four-particle amplitude at two loops.