arXiv subjects

Emmanuel Floratos

Publications and source records attributed to Emmanuel Floratos.

28 records · Page 2Linked to original sources

arXiv2014

Large-Spin Expansions of GKP Strings

We demonstrate that the large-spin expansion of the energy of Gubser-Klebanov-Polyakov (GKP) strings that rotate in RxS2 and AdS3 can be expressed in terms of Lambert's W-function. We compute the leading, subleading and next-to-subleading series of exponential corrections to the infinite-volume dispersion relation of GKP strings that rotate in RxS2. These strings are dual to certain long operators of N=4 SYM theory and provide their scaling dimensions at strong coupling. We also show that the strings obey a short-long (strings) duality. For the folded GKP strings that spin inside AdS3 and are dual to twist-2 operators, we confirm the known formulas for the leading and next-to-leading coefficients of their anomalous dimensions and derive the corresponding expressions for the next-to-next-to-leading coefficients.

hep-th↗

arXiv2013

Stringy Membranes in AdS/CFT

We study membrane configurations in AdS_{7/4}xS^{4/7}. The membranes are wrapped around the compact manifold S^{4/7} and are dynamically equivalent to bosonic strings in AdS_5. We thus conveniently identify them as "Stringy Membranes". For the case of AdS_7xS^4, their construction is carried out by embedding the Polyakov action for classical bosonic strings in AdS_5, into the corresponding membrane action. Therefore, every string configuration in AdS_5 can be realized by an appropriately chosen stringy membrane in AdS_7xS^4. We discuss the possibility of this being also the case for stringy membranes in AdS_4xS^7/Z^k (k > 1 or k = 1). By performing a stability analysis to the constructed solutions, we find that the (membrane) fluctuations along their transverse directions are organized in multiple Lamé stability bands and gaps in the space of parameters of the configurations. In this membrane picture, strings exhibit a single band/gap structure.

hep-th↗

arXiv2012

Scaling Properties of the Lorenz System and Dissipative Nambu Mechanics

In the framework of Nambu Mechanics, we have recently argued that Non-Hamiltonian Chaotic Flows in $ R^{3} $, are dissipation induced deformations, of integrable volume preserving flows, specified by pairs of Intersecting Surfaces in $R^{3}$. In the present work we focus our attention to the Lorenz system with a linear dissipative sector in its phase space dynamics. In this case the Intersecting Surfaces are Quadratic. We parametrize its dissipation strength through a continuous control parameter $ε$, acting homogeneously over the whole 3-dim. phase space. In the extended $ε$-Lorenz system we find a scaling relation between the dissipation strength $ ε$ and Reynolds number parameter r . It results from the scale covariance, we impose on the Lorenz equations under arbitrary rescalings of all its dynamical coordinates. Its integrable limit, ($ ε= 0 $, \ fixed r), which is described in terms of intersecting Quadratic Nambu "Hamiltonians" Surfaces, gets mapped on the infinite value limit of the Reynolds number parameter (r $\rightarrow \infty,\ ε= 1$). In effect weak dissipation, through small $ε$ values, generates and controls the well explored Route to Chaos in the large r-value regime. The non-dissipative $ε=0 $ integrable limit is therefore the gateway to Chaos for the Lorenz system.

nlin.CD↗

arXiv2011

Matrix Quantization of Turbulence

Based on our recent work on Quantum Nambu Mechanics $\cite{af2}$, we provide an explicit quantization of the Lorenz chaotic attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices in $ R^{3}$. For the volume preserving part, they satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Matrix Lorenz system develop fast decoherence to N independent Lorenz attractors. On the other hand there is a weak dissipation regime, where the quantum mechanical properties of the volume preserving non-dissipative sector survive for long times.

hep-th↗

arXiv2009

Strange Attractors in Dissipative Nambu Mechanics : Classical and Quantum Aspects

We extend the framework of Nambu-Hamiltonian Mechanics to include dissipation in $R^{3}$ phase space. We demonstrate that it accommodates the phase space dynamics of low dimensional dissipative systems such as the much studied Lorenz and Rössler Strange attractors, as well as the more recent constructions of Chen and Leipnik-Newton. The rotational, volume preserving part of the flow preserves in time a family of two intersecting surfaces, the so called {\em Nambu Hamiltonians}. They foliate the entire phase space and are, in turn, deformed in time by Dissipation which represents their irrotational part of the flow. It is given by the gradient of a scalar function and is responsible for the emergence of the Strange Attractors. Based on our recent work on Quantum Nambu Mechanics, we provide an explicit quantization of the Lorenz attractor through the introduction of Non-commutative phase space coordinates as Hermitian $ N \times N $ matrices in $ R^{3}$. They satisfy the commutation relations induced by one of the two Nambu Hamiltonians, the second one generating a unique time evolution. Dissipation is incorporated quantum mechanically in a self-consistent way having the correct classical limit without the introduction of external degrees of freedom. Due to its volume phase space contraction it violates the quantum commutation relations. We demonstrate that the Heisenberg-Nambu evolution equations for the Quantum Lorenz system give rise to an attracting ellipsoid in the $3 N^{2}$ dimensional phase space.

nlin.CD↗

arXiv2008

Nambu-Lie 3-Algebras on Fuzzy 3-Manifolds

We consider Nambu-Poisson 3-algebras on three dimensional manifolds $ {\cal M}_{3} $, such as the Euclidean 3-space $R^{3}$, the 3-sphere $S^{3}$ as well as the 3-torus $T^{3}$. We demonstrate that in the Clebsch-Monge gauge, the Lie algebra of volume preserving diffeomorphisms $SDiff({\cal M}_{3})$ is identical to the Nambu-Poisson algebra on ${\cal M}_{3}$. Moreover the fundamental identity for the Nambu 3-bracket is just the commutation relation of $ SDiff({\cal M}_{3})$. We propose a quantization prescription for the Nambu-Poisson algebra which provides us with the correct classical limit. As such it possesses all of the expected classical properties constituting, in effect, a concrete representation of Nambu-Lie 3-algebras.

hep-th↗

arXiv2007

Euler Top Dynamics of Nambu-Goto P-Branes

We propose a method to obtain new exact solutions of spinning p-branes in flat space-times for any p, which manifest themselves as higher dimensional Euler Tops and minimize their energy functional. We provide concrete examples for the case of spherical topology S^{2}, S^{3} and rotational symmetry \prod_{i}SO(q_{i}). In the case of toroidal topology T^{2}, T^{3} the rotational symmetry is \prod SU(q_{i}) and m target dimensions are compactified on the torus T^{m} . By double dimensional reduction the Light Cone Hamiltonians of T^{2}, T^{3} reduce to those of closed string S^{1} and T^{2} membranes respectively. The solutions are interpreted as non-perturbative spinning soliton states of type IIA-IIB superstrings.

hep-th↗

arXiv2006

MSSM GUT String Vacua, Split Supersymmetry and Fluxes

We show that previous proposals to accommodate the MSSM with string theory N=0 non-supersymmetric compactifications coming from intersecting D6-branes may be made fully consistent with the cancellation of RR tadpoles. In this respect we present the first examples of non-supersymmetric string Pati-Salam model vacua with starting observable gauge group $SU(4)_c \t SU(2)_L \t SU(2)_R$ (SU(2) from Sp(2)'s) that accommodate the spectrum of the 3 generation MSSM with a gauged baryon number with all extra exotics (either chiral or non-chiral) becoming massive and all MSSM Yukawas realized. The N=1 supersymmetry of the visible sector is broken by an extra supersymmetry messenger breaking sector that preserves a different N$^{\prime}$=1 susy, exhibiting the first examples of stringy gauge mediated models. Due to the high scale of the models, these models are also the first realistic examples of carriers of stringy split supersymmetry exhibiting universal slepton/squark masses, massive string scale gauginos, {\em unification of SU(3), SU(2) gauge couplings at} $2.04 \times 10^{16}$ GeV, a stable proton and the appearance of a landscape split SM with chiral fermions and only Higgsinos below the scale of susy breaking; the LSP neutralino candidate could also be only Higgsino or Higgsino-Wino mixture. We also add RR, NS and metric fluxes as every intersecting D-brane model without fluxes can be accommodated in the presence of fluxes. The addition of metric fluxes in the toroidal lattice also stabilizes the expected real parts of all in AdS closed string moduli (modulo D-term affects), leaving unfixed only the imaginary parts of Kähler moduli.

hep-th↗

arXiv2003

SU(5) Unified Theories from Intersecting Branes

We discuss the first string theory examples of three generation non-supersymmetric SU(5) and {\em flipped} SU(5) GUTS, which break to the Standard model at low energy, without extra matter and/or gauge group factors. Our GUT examples are based on IIA $Z_3$ orientifolds with D6-branes intersecting at non-trivial angles. These theories necessarily satisfy RR tadpoles and are free of NSNS tadpoles as the complex structure moduli are frozen (even though a dilaton tadpole remains) to discrete values. We identify appropriately the bifundamental Higgses responsible for electroweak symmetry breaking. In this way, the neutrino see-saw mechanism get nicely realized in these constructions. Moreover, as baryon number is not a gauged symmetry gauge mediated dimension six operators do contribute to proton decay; however proton lifetime may be safely enhanced by appropriately choosing a high GUT scale. An accompanying natural doublet-triplet splitting guarantees the suppression of scalar mediated proton decay modes and the stability of triplet scalar masses against higher dimensional non-renormalizable operators.

hep-th↗

arXiv2003

Scaling Violations in Yang-Mills Theories and Strings in AdS_5

String solitons in AdS_5 contain information of N=4 SUSY Yang-Mills theories on the boundary. Recent proposals for rotating string solitons reproduce the spectrum for anomalous dimensions of Wilson operators for the boundary theory. There are possible extensions of this duality for lower supersymmetric and even for non-supesymmetric Yang-Mills theories. We explicitly demonstrate that the supersymmetric anomalous dimensions of Wilson operators in N=0,1 Yang-Mills theories behave, for large spin J, at the two-loop level in perturbation theory, like log J. We compile the analytic one- and two-loop results for the N=0 case which is known in the literature, as well as for the N=1 case which seems to be missing.

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