21,542 research outputs found

### Large N and double scaling limits in two dimensions

Recently, the author has constructed a series of four dimensional
non-critical string theories with eight supercharges, dual to theories of light
electric and magnetic charges, for which exact formulas for the central charge
of the space-time supersymmetry algebra as a function of the world-sheet
couplings were obtained. The basic idea was to generalize the old matrix model
approach, replacing the simple matrix integrals by the four dimensional matrix
path integrals of N=2 supersymmetric Yang-Mills theory, and the Kazakov
critical points by the Argyres-Douglas critical points. In the present paper,
we study qualitatively similar toy path integrals corresponding to the two
dimensional N=2 supersymmetric non-linear sigma model with target space CP^n
and twisted mass terms. This theory has some very strong similarities with N=2
super Yang-Mills, including the presence of critical points in the vicinity of
which the large n expansion is IR divergent. The model being exactly solvable
at large n, we can study non-BPS observables and give full proofs that double
scaling limits exist and correspond to universal continuum limits. A complete
characterization of the double scaled theories is given. We find evidence for
dimensional transmutation of the string coupling in some non-critical string
theories. We also identify en passant some non-BPS particles that become
massless at the singularities in addition to the usual BPS states.Comment: 38 pages, including an introductory section that makes the paper
self-contained, two figures and one appendix; v2: typos correcte

### Microscopic quantum superpotential in N=1 gauge theories

We consider the N=1 super Yang-Mills theory with gauge group U(N), adjoint
chiral multiplet X and tree-level superpotential Tr W(X). We compute the
quantum effective superpotential W_mic as a function of arbitrary off-shell
boundary conditions at infinity for the scalar field X. This effective
superpotential has a remarkable property: its critical points are in one-to-one
correspondence with the full set of quantum vacua of the theory, providing in
particular a unified picture of solutions with different ranks for the low
energy gauge group. In this sense, W_mic is a good microscopic effective
quantum superpotential for the theory. This property is not shared by other
quantum effective superpotentials commonly used in the literature, like in the
strong coupling approach or the glueball superpotentials. The result of this
paper is a first step in extending Nekrasov's microscopic derivation of the
Seiberg-Witten solution of N=2 super Yang-Mills theories to the realm of N=1
gauge theories.Comment: 23 pages, 1 figure; typos corrected, version to appear in JHE

### The Proof of the Dijkgraaf-Vafa Conjecture and application to the mass gap and confinement problems

Using generalized Konishi anomaly equations, it is known that one can
express, in a large class of supersymmetric gauge theories, all the chiral
operators expectation values in terms of a finite number of a priori arbitrary
constants. We show that these constants are fully determined by the requirement
of gauge invariance and an additional anomaly equation. The constraints so
obtained turn out to be equivalent to the extremization of the Dijkgraaf-Vafa
quantum glueball superpotential, with all terms (including the
Veneziano-Yankielowicz part) unambiguously fixed. As an application, we fill
non-trivial gaps in existing derivations of the mass gap and confinement
properties in super Yang-Mills theories.Comment: 31 pages, 1 figure; v2: typos corrected; references, a note on
Kovner-Shifman vacua (section 4.3) and a few clarifying comments in Section 3
added; v3: cosmetic changes, JHEP versio

### Glueball operators and the microscopic approach to N=1 gauge theories

We explain how to generalize Nekrasov's microscopic approach to N=2 gauge
theories to the N=1 case, focusing on the typical example of the U(N) theory
with one adjoint chiral multiplet X and an arbitrary polynomial tree-level
superpotential Tr W(X). We provide a detailed analysis of the generalized
glueball operators and a non-perturbative discussion of the Dijkgraaf-Vafa
matrix model and of the generalized Konishi anomaly equations. We compute in
particular the non-trivial quantum corrections to the Virasoro operators and
algebra that generate these equations. We have performed explicit calculations
up to two instantons, that involve the next-to-leading order corrections in
Nekrasov's Omega-background.Comment: 38 pages, 1 figure and 1 appendix included; v2: typos and the list of
references corrected, version to appear in JHE

### Intermixture of extended edge and localized bulk energy levels in macroscopic Hall systems

We study the spectrum of a random Schroedinger operator for an electron
submitted to a magnetic field in a finite but macroscopic two dimensional
system of linear dimensions equal to L. The y direction is periodic and in the
x direction the electron is confined by two smooth increasing boundary
potentials. The eigenvalues of the Hamiltonian are classified according to
their associated quantum mechanical current in the y direction. Here we look at
an interval of energies inside the first Landau band of the random operator for
the infinite plane. In this energy interval, with large probability, there
exist O(L) eigenvalues with positive or negative currents of O(1). Between each
of these there exist O(L^2) eigenvalues with infinitesimal current
O(exp(-cB(log L)^2)). We explain what is the relevance of this analysis to the
integer quantum Hall effect.Comment: 29 pages, no figure

### Diffusive shock acceleration in extragalactic jets

We calculate the temporal evolution of distributions of relativistic
electrons subject to synchrotron and adiabatic processes and Fermi-like
acceleration in shocks. The shocks result from Kelvin-Helmholtz instabilities
in the jet. Shock formation and particle acceleration are treated in a
self-consistent way by means of a numerical hydrocode. We show that in our
model the number of relativistic particles is conserved during the evolution,
with no need of further injections of supra-thermal particles after the initial
one. From our calculations, we derive predictions for values and trends of
quantities like the spectral index and the cutoff frequency that can be
compared with observations.Comment: 12 pages containing 7 postscript figures; uses A&A macros. Accepted
for publication in Astronomy and Astrophysic

### Long-lived Bloch oscillations with bosonic Sr atoms and application to gravity measurement at micrometer scale

We report on the observation of Bloch oscillations on the unprecedented time
scale of severalseconds. The experiment is carried out with ultra-cold bosonic
strontium-88 loaded into a vertical optical standing wave. The negligible
atom-atom elastic cross section and the absence of spin makes $^{88}$Sr an
almost ideal Bose gas insensitive to typical mechanisms of decoherence due to
thermalization and to external stray fields. The small size enables precision
measurements of forces at micrometer scale. This is a challenge in physics for
studies of surfaces, Casimir effects, and searches for deviations from
Newtonian gravity predicted by theories beyond the standard model

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