3,229 research outputs found
Weak Decoupling Duality and Quantum Identification
If a quantum system is subject to noise, it is possible to perform quantum
error correction reversing the action of the noise if and only if no
information about the system's quantum state leaks to the environment. In this
article, we develop an analogous duality in the case that the environment
approximately forgets the identity of the quantum state, a weaker condition
satisfied by epsilon-randomizing maps and approximate unitary designs.
Specifically, we show that the environment approximately forgets quantum states
if and only if the original channel approximately preserves pairwise fidelities
of pure inputs, an observation we call weak decoupling duality. Using this
tool, we then go on to study the task of using the output of a channel to
simulate restricted classes of measurements on a space of input states. The
case of simulating measurements that test whether the input state is an
arbitrary pure state is known as equality testing or quantum identification. An
immediate consequence of weak decoupling duality is that the ability to perform
quantum identification cannot be cloned. We furthermore establish that the
optimal amortized rate at which quantum states can be identified through a
noisy quantum channel is equal to the entanglement-assisted classical capacity
of the channel, despite the fact that the task is quantum, not classical, and
entanglement-assistance is not allowed. In particular, this rate is strictly
positive for every non-constant quantum channel, including classical channels.Comment: 14 pages; v2 has some remarks added and inaccuracies corrected; v3
has new title, improved presentation and additional references; v4 is the
final, accepted version (to appear in IEEE IT), title changed once more and
numerous improvements made - the main one being that we can now show that
nontrivial amortization is necessary in erasure channel
Deriving N=2 S-dualities from Scaling for Product Gauge Groups
S-dualities in scale invariant N=2 supersymmetric field theories with product
gauge groups are derived by embedding those theories in asymptotically free
theories with higher rank gauge groups. S-duality transformations on the
couplings of the scale invariant theory follow from the geometry of the
embedding of the scale invariant theory in the Coulomb branch of the
asymptotically free theory.Comment: 19 pages latex and 1 figure using psfig.sty. References adde
Non-commutative solitons and strong-weak duality
Some properties of the non-commutative versions of the sine-Gordon model
(NCSG) and the corresponding massive Thirring theories (NCMT) are studied. Our
method relies on the NC extension of integrable models and the master
Lagrangian approach to deal with dual theories. The master Lagrangians turn out
to be the NC versions of the so-called affine Toda model coupled to matter
fields (NCATM) associated to the group GL(2), in which the Toda field belongs
to certain representations of either or corresponding
to the Lechtenfeld et al. (NCSG) or Grisaru-Penati (NCSG) proposals
for the NC versions of the sine-Gordon model, respectively. Besides, the
relevant NCMT models are written for two (four) types of Dirac fields
corresponding to the Moyal product extension of one (two) copy(ies) of the
ordinary massive Thirring model. The NCATM models share the same
one-soliton (real Toda field sector of model 2) exact solutions, which are
found without expansion in the NC parameter for the corresponding Toda
and matter fields describing the strong-weak phases, respectively. The
correspondence NCSG NCMT is promising since it is
expected to hold on the quantum level.Comment: 24 pages, 1 fig., LaTex. Typos in star products of eqs. (3.11)-(3.13)
and footnote 1 were corrected. Version to appear in JHE
Thermal DBI action for the D3-brane at weak and strong coupling
We study the effective action for finite-temperature D3-branes with an
electromagnetic field at weak and strong coupling. We call this action the
thermal DBI action. Comparing at low temperature the leading correction
for the thermal DBI action at weak and strong coupling we find that the
factor well-known from the AdS/CFT correspondence extends to the case of
arbitrary electric and magnetic fields on the D3-brane. We investigate the
reason for this by taking the decoupling limit in both the open and the closed
string descriptions thus showing that the AdS/CFT correspondence extends to the
case of arbitrary constant electric and magnetic fields on the D3-brane.Comment: 30 pages, no figure
Exotic Non-Supersymmetric Gauge Dynamics from Supersymmetric QCD
We extend Seiberg's qualitative picture of the behavior of supersymmetric QCD
to nonsupersymmetric models by adding soft supersymmetry breaking terms. In
this way, we recover the standard vacuum of QCD with flavors and
colors when . However, for , we find new exotic
states---new vacua with spontaneously broken baryon number for , and
a vacuum state with unbroken chiral symmetry for . These exotic
vacua contain massless composite fermions and, in some cases, dynamically
generated gauge bosons. In particular Seiberg's electric-magnetic duality seems
to persist also in the presence of (small) soft supersymmetry breaking. We
argue that certain, specially tailored, lattice simulations may be able to
detect the novel phenomena. Most of the exotic behavior does not survive the
decoupling limit of large SUSY breaking parameters.Comment: 36 pages, latex + 2 figures (uuencoded ps
Holography, Singularities on Orbifolds and 4D N=2 SQCD
Type II string theory compactified on a Calabi-Yau manifold, with a
singularity modeled by a hypersurface in an orbifold, is considered. In the
limit of vanishing string coupling, one expects a non gravitational theory
concentrated at the singularity. It is proposed that this theory is
holographicly dual to a family of ``non-critical'' superstring vacua,
generalizing a previous proposal for hypersurfaces in flat space. It is argued
that a class of such singularities is relevant for the study of non-trivial IR
fixed points that appear in the moduli space of four-dimensional N=2 SQCD:
SU(N_c) gauge theory with matter in the fundamental representation. This
includes the origin in the moduli space of the SU(N_c) gauge theory with
N_f=2N_c fundamentals. The 4D IR fixed points are studied using the
anti-holographic description and the results agree with information available
from gauge theory.Comment: 33 pages (Latex
N=2 supersymmetric QCD and elliptic potentials
We investigate the relation between the four dimensional N=2 SU(2) super
Yang-Mills theory with four fundamental flavors and the quantum mechanics model
with Treibich-Verdier potential described by the Heun equation in the elliptic
form. We study the precise correspondence of quantities in the gauge theory and
the quantum mechanics model. An iterative method is used to obtain the
asymptotic expansion of the spectrum for the Schr\"{o}dinger operator, we are
able to fix the precise relation between the energy spectrum and the instanton
partition function of the gauge theory. We also study asymptotic expansions for
the spectrum which correspond to the strong coupling regions of the
Seiberg-Witten theory.Comment: Latex, 29pp, published version, content restructured and simplifie
DLCQ and Plane Wave Matrix Big Bang Models
We study the generalisations of the Craps-Sethi-Verlinde matrix big bang
model to curved, in particular plane wave, space-times, beginning with a
careful discussion of the DLCQ procedure. Singular homogeneous plane waves are
ideal toy-models of realistic space-time singularities since they have been
shown to arise universally as their Penrose limits, and we emphasise the role
played by the symmetries of these plane waves in implementing the flat space
Seiberg-Sen DLCQ prescription for these curved backgrounds. We then analyse
various aspects of the resulting matrix string Yang-Mills theories, such as the
relation between strong coupling space-time singularities and world-sheet
tachyonic mass terms. In order to have concrete examples at hand, in an
appendix we determine and analyse the IIA singular homogeneous plane wave -
null dilaton backgrounds.Comment: 29 pages, v2: reference added + minor cosmetic correction
Transformations of Spherical Blocks
We further explore the correspondence between N=2 supersymmetric SU(2) gauge
theory with four flavors on epsilon-deformed backgrounds and conformal field
theory, with an emphasis on the epsilon-expansion of the partition function
natural from a topological string theory point of view. Solving an appropriate
null vector decoupling equation in the semi-classical limit allows us to
express the instanton partition function as a series in quasi-modular forms of
the group Gamma(2), with the expected symmetry Weyl group of SO(8) semi-direct
S_3. In the presence of an elementary surface operator, this symmetry is
enhanced to an action of the affine Weyl group of SO(8) semi-direct S_4 on the
instanton partition function, as we demonstrate via the link between the null
vector decoupling equation and the quantum Painlev\'e VI equation.Comment: 31 pages, 1 figure; v2: typos corrected, references adde
- …