683 research outputs found
The One-Loop Spectral Problem of Strongly Twisted =4 Super Yang-Mills Theory
We investigate the one-loop spectral problem of -twisted, planar
=4 Super Yang-Mills theory in the double-scaling limit of
infinite, imaginary twist angle and vanishing Yang-Mills coupling constant.
This non-unitary model has recently been argued to be a simpler version of
full-fledged planar =4 SYM, while preserving the latter model's
conformality and integrability. We are able to derive for a number of sectors
one-loop Bethe equations that allow finding anomalous dimensions for various
subsets of diagonalizable operators. However, the non-unitarity of these
deformed models results in a large number of non-diagonalizable operators,
whose mixing is described by a very complicated structure of non-diagonalizable
Jordan blocks of arbitrarily large size and with a priori unknown generalized
eigenvalues. The description of these blocks by methods of integrability
remains unknown.Comment: 33 page
The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
We argue that existing methods for the perturbative computation of anomalous dimensions and the disentanglement of mixing in N = 4 gauge theory can be considerably simplified, systematized and extended by focusing on the theory’s dilatation operator. The effciency of the method is first illustrated at the oneloop level for general non-derivative scalar states. We then go on to derive, for pure scalar states, the two-loop structure of the dilatation operator. This allows us to obtain a host of new results. Among these are an infinite number of previously unknown two-loop anomalous dimensions, new subtleties concerning ’t Hooft’s large N expansion due to mixing effects of degenerate single and multiple trace states, two-loop tests of various protected operators, as well as two-loop nonplanar results for two-impurity operators in BMN gauge theory. We also put to use the recently discovered integrable spin chain description of the planar one-loop dilatation operator and show that the associated Yang-Baxter equation explains the existence of a hitherto unknown planar “axial” symmetry between infinitely many gauge theory states. We present evidence that this integrability can be extended to all loops, with intriguing consequences for gauge theory, and that it leads to a novel integrable deformation of the XXX Heisenberg spin chain. Assuming that the integrability structure extends to more than two loops, we determine the planar three-loop contribution to the dilatation operator
Probing molecular dynamics at the nanoscale via an individual paramagnetic center
Understanding the dynamics of molecules adsorbed to surfaces or confined to
small volumes is a matter of increasing scientific and technological
importance. Here, we demonstrate a pulse protocol using individual paramagnetic
nitrogen vacancy (NV) centers in diamond to observe the time evolution of 1H
spins from organic molecules located a few nanometers from the diamond surface.
The protocol records temporal correlations among the interacting 1H spins, and
thus is sensitive to the local system dynamics via its impact on the nuclear
spin relaxation and interaction with the NV. We are able to gather information
on the nanoscale rotational and translational diffusion dynamics by carefully
analyzing the time dependence of the NMR signal. Applying this technique to
various liquid and solid samples, we find evidence that liquid samples form a
semi-solid layer of 1.5 nm thickness on the surface of diamond, where
translational diffusion is suppressed while rotational diffusion remains
present. Extensions of the present technique could be adapted to highlight the
chemical composition of molecules tethered to the diamond surface or to
investigate thermally or chemically activated dynamical processes such as
molecular folding
Baxter Operators and Hamiltonians for "nearly all" Integrable Closed gl(n) Spin Chains
We continue our systematic construction of Baxter Q-operators for spin chains, which is based on certain degenerate solutions of the Yang-Baxter equation. Here we generalize our approach from the fundamental representation of gl(n) to generic finite-dimensional representations in quantum space. The results equally apply to non-compact representations of highest or lowest weight type. We furthermore fill an apparent gap in the literature, and provide the nearest-neighbor Hamiltonians of the spin chains in question for all cases where the gl(n) representations are described by rectangular Young diagrams, as well as for their infinite-dimensional generalizations. They take the form of digamma functions depending on operator-valued shifted weights
Oscillator construction of su(n|m) Q-operators
We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded Yang-Baxter equation, leading to an amalgam of bosonic and fermionic oscillator algebras. Our approach is fully algebraic, and leads to the exact solution of the associated compact spin chains while avoiding Bethe ansatz techniques. It furthermore elucidates the algebraic and combinatorial structures underlying the system of nested Bethe equations. Finally, our construction naturally reproduces the representation, due to Z. Tsuboi, of the hierarchy of Baxter Q-operators in terms of hypercubic Hasse diagrams. © 2011 Elsevier B.V
A shortcut to the Q-operator
Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2 Heisenberg-Bethe XXX spin chain. Here we attempt to fill this gap and show how two linearly independent operatorial solutions to Baxter's TQ equation may be constructed as commuting transfer matrices if a twist field is present. The latter are obtained by tracing over infinitely many oscillator states living in the auxiliary channel of an associated monodromy matrix. We furthermore compare our approach to and differentiate it from earlier articles addressing the problem of the construction of the Q-operator for the XXX chain. Finally we speculate on the importance of Q-operators for the physical interpretation of recent proposals for the Y-system of AdS/CFT. © 2010 IOP Publishing Ltd and SISSA
Harmonic R matrices for scattering amplitudes and spectral regularization
Planar N=4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories. © 2013 American Physical Society
Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory
Planar N= 4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N= 4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions. © 2014 The Author(s)
Yang-Lee Zeros of the Ising model on Random Graphs of Non Planar Topology
We obtain in a closed form the 1/N^2 contribution to the free energy of the
two Hermitian N\times N random matrix model with non symmetric quartic
potential. From this result, we calculate numerically the Yang-Lee zeros of the
2D Ising model on dynamical random graphs with the topology of a torus up to
n=16 vertices. They are found to be located on the unit circle on the complex
fugacity plane. In order to include contributions of even higher topologies we
calculated analytically the nonperturbative (sum over all genus) partition
function of the model Z_n = \sum_{h=0}^{\infty} \frac{Z_n^{(h)}}{N^{2h}} for
the special cases of N=1,2 and graphs with n\le 20 vertices. Once again the
Yang-Lee zeros are shown numerically to lie on the unit circle on the complex
fugacity plane. Our results thus generalize previous numerical results on
random graphs by going beyond the planar approximation and strongly indicate
that there might be a generalization of the Lee-Yang circle theorem for
dynamical random graphs.Comment: 19 pages, 7 figures ,1 reference and a note added ,To Appear in
Nucl.Phys
- …