A Deformation of Twistor Space and a Chiral Mass Term in N=4 Super Yang-Mills Theory

Super twistor space admits a certain (super) complex structure deformation that preserves the Poincare subgroup of the symmetry group PSL(4|4) and depends on 10 parameters. In a previous paper [hep-th/0502076], it was proposed that in twistor string theory this deformation corresponds to augmenting N=4 super Yang-Mills theory by a mass term for the left-chirality spinors. In this paper we analyze this proposal in more detail. We calculate 4-particle scattering amplitudes of fermions, gluons and scalars and show that they are supported on holomorphic curves in the deformed twistor space.Comment: 52 pages, 15 figure

Correlated Errors in Quantum Error Corrections

We show that errors are not generated correlatedly provided that quantum bits do not directly interact with (or couple to) each other. Generally, this no-qubits-interaction condition is assumed except for the case where two-qubit gate operation is being performed. In particular, the no-qubits-interaction condition is satisfied in the collective decoherence models. Thus, errors are not correlated in the collective decoherence. Consequently, we can say that current quantum error correcting codes which correct single-qubit-errors will work in most cases including the collective decoherence.Comment: no correction, 3 pages, RevTe

Inhomogeneously doped two-leg ladder systems

A chemical potential difference between the legs of a two-leg ladder is found to be harmful for Cooper pairing. The instability of superconductivity in such systems is analyzed by compairing results of various analytical and numerical methods. Within a strong coupling approach for the t-J model, supplemented by exact numerical diagonalization, hole binding is found unstable beyond a finite, critical chemical potential difference. The spinon-holon mean field theory for the t-J model shows a clear reduction of the the BCS gaps upon increasing the chemical potential difference leading to a breakdown of superconductivity. Based on a renormalization group approach and Abelian bosonization, the doping dependent phase diagram for the weakly interacting Hubbard model with different chemical potentials was determined.Comment: Revtex4, 11 pages, 7 figure

On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge theory with symmetric or antisymmetric tensor. We study the algebra of chiral rotations of the matter field and show that it does not receive nonperturbative corrections. The algebra implies Wess-Zumino consistency conditions for the generalized Konishi anomaly which are used to show that the anomaly does not receive nonperturbative corrections for superpotentials of degree less than 2l+1 where 2l=3c(Adj)-c(R) is the one-loop beta function coefficient. The superpotentials of higher degree can be nonperturbatively renormalized because of the ambiguities in the UV completion of the gauge theory. We discuss the implications for the Dijkgraaf-Vafa conjecture.Comment: 23 page

The Topological B-model on a Mini-Supertwistor Space and Supersymmetric Bogomolny Monopole Equations

In the recent paper hep-th/0502076, it was argued that the open topological B-model whose target space is a complex (2|4)-dimensional mini-supertwistor space with D3- and D1-branes added corresponds to a super Yang-Mills theory in three dimensions. Without the D1-branes, this topological B-model is equivalent to a dimensionally reduced holomorphic Chern-Simons theory. Identifying the latter with a holomorphic BF-type theory, we describe a twistor correspondence between this theory and a supersymmetric Bogomolny model on R^3. The connecting link in this correspondence is a partially holomorphic Chern-Simons theory on a Cauchy-Riemann supermanifold which is a real one-dimensional fibration over the mini-supertwistor space. Along the way of proving this twistor correspondence, we review the necessary basic geometric notions and construct action functionals for the involved theories. Furthermore, we discuss the geometric aspect of a recently proposed deformation of the mini-supertwistor space, which gives rise to mass terms in the supersymmetric Bogomolny equations. Eventually, we present solution generating techniques based on the developed twistorial description together with some examples and comment briefly on a twistor correspondence for super Yang-Mills theory in three dimensions.Comment: 55 pages; v2: typos fixed, published versio

Electromagnetic Response of Layered Superconductors with Broken Lattice Inversion Symmetry

We investigate the macroscopic effects of charge density waves (CDW) and superconductivity in layered superconducting systems with broken lattice inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D) transition metal dichalcogenides (TMD). We work with the low temperature time dependent Ginzburg-Landau theory and study the coupling of lattice distortions and low energy CDW collective modes to the superconducting order parameter in the presence of electromagnetic fields. We show that superconductivity and piezoelectricity can coexist in these singular metals. Furthermore, our study indicates the nature of the quantum phase transition between a commensurate CDW phase and the stripe phase that has been observed as a function of applied pressure.Comment: 9 pages, 1 figure. Final version. Accepted in Phys.Rev.

Effective superpotential for U(N) with antisymmetric matter

We consider an N=1 U(N) gauge theory with matter in the antisymmetric representation and its conjugate, with a tree level superpotential containing at least quartic interactions for these fields. We obtain the effective glueball superpotential in the classically unbroken case, and show that it has a non-trivial N-dependence which does not factorize. We also recover additional contributions starting at order S^N from the dynamics of Sp(0) factors. This can also be understood by a precise map of this theory to an Sp(2N-2) gauge theory with antisymmetric matter.Comment: 22 pages. v2: comment (and a reference) added at the end of section 2 on low rank cases; minor typos corrected. v3: 2 footnotes added with additional clarifications; version to appear in journa

Marginal deformation of N=4 SYM and Penrose limits with continuum spectrum

We study the Penrose limit about a null geodesic with 3 equal angular momenta in the recently obtained type IIB solution dual to an exactly marginal $\gamma$-deformation of N=4 SYM. The resulting background has non-trivial NS 3-form flux as well as RR 5- and 3-form fluxes. We quantise the light-cone Green-Schwarz action and show that it exhibits a continuum spectrum. We show that this is related to the dynamics of a charged particle moving in a Landau plane with an extra interaction induced by the deformation. We interpret the results in the dual N=1 SCFT.Comment: 26 pages, 2 figures; v2: typos corrected, field theory interpretation extende

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an ($n-1$)-qubit logical state encoded in $n$ physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. In addition, universal quantum computation is possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber \emph{et al.}, Phys. Rev. Lett. 86, 4402 (2001)].Comment: 11 pages, 1 figure; minor correction

Lepton Flavour Violation in a Class of Lopsided SO(10) Models

A class of predictive SO(10) grand unified theories with highly asymmetric mass matrices, known as lopsided textures, has been developed to accommodate the observed mixing in the neutrino sector. The model class effectively determines the rate for charged lepton flavour violation, and in particular the branching ratio for $\mu -> e \gamma$, assuming that the supersymmetric GUT breaks directly to the constrained minimal supersymmetric standard model (CMSSM). We find that in light of the combined constraints on the CMSSM parameters from direct searches and from the WMAP satellite observations, the resulting predicted rate for $\mu -> e \gamma$ in this model class can be within the current experimental bounds for low $\tan \beta$, but that the next generation of $\mu -> e \gamma$ experiments would effectively rule out this model class if LFV is not detected.Comment: 23 page