A Quantum Gauge Group Approach to the 2D SU(n) WZNW Model

The canonical quantization of the WZNW model provides a complete set of exchange relations in the enlarged chiral state spaces that include the Gauss components of the monodromy matrices. Regarded as new dynamical variables, the elements of the latter cannot be identified -- they satisfy different exchange relations. Accordingly, the two dimensional theory expressed in terms of the left and right movers' fields does not automatically respect monodromy invariance. Continuing our recent analysis of the problem by gauge theory methods we conclude that physical states (on which the two dimensional field acts as a single valued operator) are invariant under the (permuted) coproduct of the left and right $U_q(sl(n))$. They satisfy additional constraints fully described for n=2.Comment: 10 pages, LATEX (Proposition 4.2 corrected, one reference added

Extended su(2)_k and restricted U_q sl(2)

Global gauge symmetry becomes more intricate in low dimensional QFT. We survey the mathematical concepts leading to the relevant analogues of the (D=4) Doplicher-Haag-Roberts theory of superselection sectors and internal symmetry. We also review a recently uncovered duality between braid and quantum group representations in an extension of the chiral su(2)_k WZNW model for nonnegative integer level k.Comment: 11 pages, extended version of a talk at the International Workshop "Lie Theory and Its Applications in Physics VII" (Varna, Bulgaria, June 2007), to appear in the proceedings (eds. V. Dobrev et.al., Heron Press, Sofia

Indecomposable U_q(sl_n) modules for q^h = -1 and BRS intertwiners

A class of indecomposable representations of U_q(sl_n) is considered for q an even root of unity (q^h = -1) exhibiting a similar structure as (height h) indecomposable lowest weight Kac-Moody modules associated with a chiral conformal field theory. In particular, U_q(sl_n) counterparts of the Bernard-Felder BRS operators are constructed for n=2,3. For n=2 a pair of dual d_2(h) = h dimensional U_q(sl_2) modules gives rise to a 2h-dimensional indecomposable representation including those studied earlier in the context of tensor product expansions of irreducible representations. For n=3 the interplay between the Poincare'-Birkhoff-Witt and (Lusztig) canonical bases is exploited in the study of d_3(h) = h(h+1)(2h+1)/6 dimensional indecomposable modules and of the corresponding intertwiners

Chiral zero modes of the SU(n) WZNW model

We define the chiral zero modes' phase space of the G=SU(n) Wess-Zumino-Novikov-Witten (WZNW) model as an (n-1)(n+2)-dimensional manifold M_q equipped with a symplectic form involving a special 2-form - the Wess-Zumino (WZ) term - which depends on the monodromy M. This classical system exhibits a Poisson-Lie symmetry that evolves upon quantization into an U_q(sl_n) symmetry for q a primitive even root of 1. For each constant solution of the classical Yang-Baxter equation (CYBE) we write down explicitly a corresponding WZ term and invert the symplectic form thus computing the Poisson bivector of the system. The resulting Poisson brackets appear as the classical counterpart of the exchange relations of the quantum matrix algebra studied previously. We argue that it is advantageous to equate the determinant D of the zero modes' matrix to a pseudoinvariant under permutations polynomial in the SU(n) weights, rather than to adopt the familiar convention D=1

Neural correlates of finger gnosis

Neuropsychological studies have described patients with a selective impairment of finger identification in association with posterior parietal lesions. However, evidence of the role of these areas in finger gnosis from studies of the healthy human brain is still scarce. Here we used functional magnetic resonance imaging to identify the brain network engaged in a novel finger gnosis task, the intermanual in-between task (IIBT), in healthy participants. Several brain regions exhibited a stronger blood oxygenation level-dependent (BOLD) response in IIBT than in a control task that did not explicitly rely on finger gnosis but used identical stimuli and motor responses as the IIBT. The IIBT involved stronger signal in the left inferior parietal lobule (IPL), bilateral precuneus (PCN), bilateral premotor cortex, and left inferior frontal gyrus. In all regions, stimulation of nonhomologous fingers of the two hands elicited higher BOLD signal than stimulation of homologous fingers. Only in the left anteromedial IPL (a-mIPL) and left PCN did signal strength decrease parametrically from nonhomology, through partial homology, to total homology with stimulation delivered synchronously to the two hands. With asynchronous stimulation, the signal was stronger in the left a-mIPL than in any other region, possibly indicating retention of task-relevant information. We suggest that the left PCN may contribute a supporting visuospatial representation via its functional connection to the right PCN. The a-mIPL may instead provide the core substrate of an explicit bilateral body structure representation for the fingers that when disrupted can produce the typical symptoms of finger agnosia

Operator realization of the SU(2) WZNW model

Decoupling the chiral dynamics in the canonical approach to the WZNW model requires an extended phase space that includes left and right monodromy variables. Earlier work on the subject, which traced back the quantum qroup symmetry of the model to the Lie-Poisson symmetry of the chiral symplectic form, left some open questions: - How to reconcile the monodromy invariance of the local 2D group valued field (i.e., equality of the left and right monodromies) with the fact that the latter obey different exchange relations? - What is the status of the quantum group symmetry in the 2D theory in which the chiral fields commute? - Is there a consistent operator formalism in the chiral and in the extended 2D theory in the continuum limit? We propose a constructive affirmative answer to these questions for G=SU(2) by presenting the chiral quantum fields as sums of chiral vertex operators and q-Bose creation and annihilation operators.Comment: 18 pages, LATE

How Biorecognition Affects the Electronic Properties of Reduced Graphene Oxide in Electrolyte‐Gated Transistor Immunosensors

Ambipolar electrolyte-gated transistors (EGTs) based on reduced graphene oxide (rGO) have been demonstrated as ultra-sensitive and highly specific immunosensors. However, the physics and chemistry ruling the device operation are still not fully unraveled. In this work, the aim is to elucidate the nature of the observed sensitivity of the device. Toward this aim, a physical–chemical model that, coupled with the experimental characterization of the rGO-EGT, allows one to quantitatively correlate the biorecognition events at the gate electrode and the electronic properties of rGO-EGT is proposed. The equilibrium of biorecognition occurring at the gate electrode is shown to determine the apparent charge neutrality point (CNP) of the rGO channel. The multiparametric analysis of the experimental transfer characteristics of rGO-EGT reveals that the recognition events modulate the CNP voltage, the excess carrier density Δn, and the quantum capacitance of rGO. This analysis also explains why hole and electron carrier mobilities, interfacial capacitance, the curvature of the transfer curve, and the transconductances are insensitive to the target concentration. The understanding of the mechanisms underlying the transistor transduction of the biorecognition events is key for the interpretation of the response of the rGO-EGT immunosensors and to guide the design of novel and more sensitive devices