Impurity non-preserving 3-point correlators of BMN operators from PP-wave holography II: Fermionic excitations

The holographic principle in the PP-wave limit proposed in our previous works is further confirmed by studying impurity non-preserving processes which contain a fermionic BMN operator with one scalar and one fermion impurities. We show that the previously proposed duality relation between the matrix elements of the three point interaction Hamiltonian in the holographic string field theory and the OPE coefficients in super-Yang–Mills theory holds to the leading order in the large μ limit. Operator mixing is required to obtain the BMN operator of definite conformal dimension which corresponds to the string state with one scalar and one fermion excitations. The mixing term plays a crucial role for our duality relation to be valid. Our results, combined with those in the previous papers, provide a positive support that our duality relation holds for the general process regardless of the kind of impurities and of whether impurities conserve or not.     

Fermionic composite models from complementarity

Composite models for (in principle massless) quarks and leptons without fundamental scalars are constructed with the aim of providing for fermionic realizations of models which include elementary bosons (by Abbott and Farhi, Casalbuoni and Gatto and Barbieri, Mohapatra and Masiero). The models use one confining unitary (subcolor) group (with left-handed fermions in the fundamental, in its conjugate, and either in the adjoint, or in the symmetric, or in the antisymmetric representation of subcolor) or two confining groups. Families may arise from discrete symmetries.     

Dynamics of quark-gluon plasma from field correlators

It is argued that strong dynamics in the quark-gluon plasma and bound states of quarks and gluons is mostly due to nonperturbative effects described by field correlators. The emphasis in the paper is made on two explicit calculations of these effects from first principles—one analytic using gluelump Green’s functions and another using independent lattice data on correlators. The resulting hadron spectra are investigated in the range T _c ≤ T < 2T _c . The spectra of charmonia, bottomonia, light s mesons, glueballs, and quark-gluon states calculated numerically are in general agreement with lattice MEM data. The possible role of these bound states in the thermodynamics of quark—gluon plasma is discussed. The text was submitted by the authors in English.     

An approach to the deduction of the finite-dimensional integrability from the infinite-dimensional integrability

A systematic method for deducing the Liouville integrability of a finite-dimensional Hamiltonian system reduced from an infinite-dimensional Hamiltonian system is proposed within the framework of the zero-curvature representation theory. Also a systematic way to treat the higher-order constraints and to obtain the associated infinitely many hierarchies of finite-dimensional integrable Hamiltonian systems is presented.     

Yangian symmetric correlators

Similarity transformations and eigenvalue relations of monodromy operators composed of Jordan–Schwinger type L matrices are considered and used to define Yangian symmetric correlators of n-dimensional theories. Explicit expressions are obtained and relations are formulated. In this way basic notions of the Quantum inverse scattering method provide a convenient formulation for high symmetry and integrability not only in lower dimensions.     

Cosmological unparticle correlators

We introduce and study an extension of the correlator of unparticle matter operators in a cosmological environment. Starting from FRW spaces we specialize to a de Sitter space–time and derive its inflationary power spectrum which we find to be almost flat. We finally investigate some consequences of requiring the existence of a unitary boundary conformal field theory in the framework of the dS/CFT correspondence.     

Fermionic atom laser

An output coupling of a magnetically trapped two-species Fermi gas to a untrapped species is considered which can be implemented using rf or optical Raman transitions. The process can be used to produce an intense output beam of fermionic atoms once the device reaches a threshold in the zero-temperature case. For finite temperatures there is no threshold, as the output current grows smoothly. This behavior, which is reminiscent of conventional optical and cavity-QED lasers, suggests the name fermionic atom laser for this device. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 1, 13–17 (10 July 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator

By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product （IWOP） of Fermi operators is used in our discussion.     

Fermionic Quantum Computation

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.     

On Fermionic Entangled State Representation and Fermionic Entangled Wigner Operator

By analogy with the bosonic bipartite entangled state we construct fermionic entangled state with the Grassmann numbers. The Wigner operator in the fermionic entangled state representation is introduced, whose marginal distributions are understood in an entangled way. The technique of integration within an ordered product (IWOP) of Fermi operators is used in our discussion.     

Fermionic Linear Optics Revisited

We provide an alternative view of the efficient classical simulatibility of fermionic linear optics in terms of Slater determinants. We investigate the generic effects of two-mode measurements on the Slater number of fermionic states. We argue that most such measurements are not capable (in conjunction with fermion linear optics) of an efficient exact implementation of universal quantum computation. Our arguments do not apply to the two-mode parity measurement, for which exact quantum computation becomes possible.     

Measures for Fermionic Integration

The formal Berezin integral for anticommuting variables is modified to a functional which can be applied directly to an infinite dimensional Grassmann algebra. Then a Gaussian measure is constructed on an extended Grassmann algebra and the functional integral is realized as integral on this measure space.     

Fermionic composite models from confining SU(2)L

A class of fermionic composite models with SU(2)_L as confining group is discussed utilizing the notion of complementarity. The models are, in some sense, fermionic realizations of the bosonic Abbott-Farhi model, avoiding fundamental scalars. Model A has SU(2)_L as confining group; model B has an additional chiral SU(M) and coincides with a model by Abbott, Fahri and Schwimmer; model C has an additional vector SU(M) and provides for a closer realization of the original basonic model.     

Topology and Fermionic Condensate

The purpose of this paper is to investigate an influence of a space-time topology on the formation of fermionic condensate 〈φφ〉 in the model with four-fermion interaction (φφ)². The value for the space-time with topology of R₁ × R₁ × S₁ is found. Moreover a relation of the value of fermionic condensate to a periodic length is studied. In this connection the possibility of a relation of the topologic deposits to structure of hadrons is discussed.     

Explicit Fermionic Tree Expansions

We express connected Fermionic Green's functions in terms of two totally explicit tree formulas. The simplest and most symmetric formula, the Brydges–Kennedy formula is compatible with Gram's inequality. The second one, the rooted formula of Abdesselam and Rivasseau, respects even better the antisymmetric structure of determinants, and allows the direct comparison of rows and columns which correspond to the mathematical implementation in Grassmann integrals of the Pauli principle. To illustrate the power of these formulas, we give a three lines proof that the radius of convergence of the Gross–Neveu theory with cutoff is independent of the number of colors, using either one or the other of these formulas.     

Fermionic quantum stochastic flows

Existence, uniqueness and, using a higher-order Fermionic Itô formula, multiplicativity are proved for even quantum stochastic flows over ₂graded C ^*-algebras driven by Fermionic noise with bounded structure maps.Work supported by EU HCM Contract CHRX-CT93-QO94.