49 research outputs found

    Exact Solution of the one-impurity quantum Hall problem

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    The problem of a non-relativistic electron in the presence of a uniform electromagnetic field and of one impurity, described by means of an Aharonov-Bohm point-like vortex, is studied. The exact solution is found and the quantum Hall's conductance turns out to be the same as in the impurity-free case. This exactly solvable model seems to give indications, concerning the possible microscopic mechanisms underlying the integer quantum Hall effect, which sensibly deviate from some proposals available in the literature.Comment: 25 pages, TeX, to appear in J. Phys.

    On the large N limit, W_\infty Strings, Star products, AdS/CFT Duality, Nonlinear Sigma Models on AdS spaces and Chern-Simons p-branes

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    It is shown that the large NN limit of SU(N) YM in curvedcurved mm-dim backgrounds can be subsumed by a higher m+nm+n dimensional gravitational theory which can be identified to an mm-dim generally invariant gauge theory of diffs NN, where NN is an nn-dim internal space (Cho, Sho, Park, Yoon). Based on these findings, a very plausible geometrical interpretation of the AdS/CFTAdS/CFT correspondence could be given. Conformally invariant sigma models in D=2nD=2n dimensions with target non-compact SO(2n,1) groups are reviewed. Despite the non-compact nature of the SO(2n,1), the classical action and Hamiltonian are positive definite. Instanton field configurations are found to correspond geometrically to conformal ``stereographic'' mappings of R2nR^{2n} into the Euclidean signature AdS2nAdS_{2n} spaces. The relation between Self Dual branes and Chern-Simons branes, High Dimensional Knots, follows. A detailed discussion on WW_\infty symmetry is given and we outline the Vasiliev procedure to construct an action involving higher spin massless fields in AdS4AdS_4. This AdS4AdS_4 spacetime higher spin theory should have a one-to-one correspondence to noncritical WW_\infty strings propagating on AdS4×S7AdS_4 \times S^7.Comment: 43 pages, Tex fil

    On the Quantization of the Abelian Chern-Simons Coefficient at Finite Temperature

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    We show that when the Abelian \CS\ theory coupled to matter fields is quantized in a vacuum with non vanishing magnetic flux (or electric charge), the requirement of gauge invariance at finite temperature leads to the quantization of the \CS\ coefficient and its quantum corrections, in a manner similar to the non-Abelian case.Facultad de Ciencias Exacta

    Non abelian bosonisation in three dimensional field theory

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    We develop a method based on the generalised St\"uckelberg prescription for discussing bosonisation in the low energy regime of the SU(2) massive Thirring model in 2+1 dimensions. For arbitrary values of the coupling parameter the bosonised theory is found to be a nonabelian gauge theory whose physical sector is explicitly obtained. In the case of vanishing coupling this gauge theory can be identified with the SU(2) Yang-Mills Chern-Simons theory in the limit when the Yang-Mills term vanishes. Bosonisation identities for the fermionic current are derived.Comment: Latex version, 14 pages; 23 reference

    Quadratic Effective Action for QED in D=2,3 Dimensions

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    We calculate the effective action for Quantum Electrodynamics (QED) in D=2,3 dimensions at the quadratic approximation in the gauge fields. We analyse the analytic structure of the corresponding nonlocal boson propagators nonperturbatively in k/m. In two dimensions for any nonzero fermion mass, we end up with one massless pole for the gauge boson . We also calculate in D=2 the effective potential between two static charges separated by a distance L and find it to be a linearly increasing function of L in agreement with the bosonized theory (massive Sine-Gordon model). In three dimensions we find nonperturbatively in k/m one massive pole in the effective bosonic action leading to screening. Fitting the numerical results we derive a simple expression for the functional dependence of the boson mass upon the dimensionless parameter e^{2}/m .Comment: 10 pages, 2 figure

    Induced Parity-Breaking Term at Finite Chemical Potential and Temparature

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    We exactly calculated the parity-odd term of the effective action induced by the fermions in 2+1 dimensions at finite chemical potential and finite temperature. It shows that gauge invariance is still respected. A more gerneral class of background configurations is considered. The knowledge of the reduced 1+1 determinant is required in order to draw exact conclusions about the gauge invariance of the parity-odd term in this latter case.Comment: 8 pages, LATEX, no figure
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