64 research outputs found
On renormalization group flows and the a-theorem in 6d
We study the extension of the approach to the a-theorem of Komargodski and
Schwimmer to quantum field theories in d=6 spacetime dimensions. The dilaton
effective action is obtained up to 6th order in derivatives. The anomaly flow
a_UV - a_IR is the coefficient of the 6-derivative Euler anomaly term in this
action. It then appears at order p^6 in the low energy limit of n-point
scattering amplitudes of the dilaton for n > 3. The detailed structure with the
correct anomaly coefficient is confirmed by direct calculation in two examples:
(i) the case of explicitly broken conformal symmetry is illustrated by the free
massive scalar field, and (ii) the case of spontaneously broken conformal
symmetry is demonstrated by the (2,0) theory on the Coulomb branch. In the
latter example, the dilaton is a dynamical field so 4-derivative terms in the
action also affect n-point amplitudes at order p^6. The calculation in the
(2,0) theory is done by analyzing an M5-brane probe in AdS_7 x S^4.
Given the confirmation in two distinct models, we attempt to use dispersion
relations to prove that the anomaly flow is positive in general. Unfortunately
the 4-point matrix element of the Euler anomaly is proportional to stu and
vanishes for forward scattering. Thus the optical theorem cannot be applied to
show positivity. Instead the anomaly flow is given by a dispersion sum rule in
which the integrand does not have definite sign. It may be possible to base a
proof of the a-theorem on the analyticity and unitarity properties of the
6-point function, but our preliminary study reveals some difficulties.Comment: 41 pages, 5 figure
M5-branes from gauge theories on the 5-sphere
We use the 5-sphere partition functions of supersymmetric Yang-Mills theories
to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be
regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a
special limit, the perturbative partition function takes the form of the
Chern-Simons partition function on S^3. With a simple non-perturbative
completion, it becomes a 6d index which captures the degeneracy of a sector of
BPS states as well as the index version of the vacuum Casimir energy. The
Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N)
gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling
behaviors of large N free energy, minor improvements, version to be published
in JHE
Z-extremization and F-theorem in Chern-Simons matter theories
The three dimensional exact R symmetry of N=2 SCFTs extremizes the partition
function localized on a three sphere. Here we verify this statement at weak
coupling. We give a detailed analysis for two classes of models. The first one
is an SU(N)_k gauge theory at large k with both fundamental and adjoint matter
fields, while the second is a flavored version of the ABJ theory, where the CS
levels are large but they do not necessarily sum up to zero. We study in both
cases superpotential deformations and compute the R charges at different fixed
points. When these fixed points are connected by an RG flow we explicitly
verify that the free energy decreases at the endpoints of the flow between the
fixed points, corroborating the conjecture of an F-theorem in three dimensions.Comment: 28 pages, 3 figures, JHEP.cls, minor corrections, references adde
On Renormalization Group Flows in Four Dimensions
We discuss some general aspects of renormalization group flows in four
dimensions. Every such flow can be reinterpreted in terms of a spontaneously
broken conformal symmetry. We analyze in detail the consequences of trace
anomalies for the effective action of the Nambu-Goldstone boson of broken
conformal symmetry. While the c-anomaly is algebraically trivial, the a-anomaly
is "non-Abelian," and leads to a positive-definite universal contribution to
the S-matrix of 2->2 dilaton scattering. Unitarity of the S-matrix results in a
monotonically decreasing function that interpolates between the Euler anomalies
in the ultraviolet and the infrared, thereby establishing the a-theorem.Comment: 24 pages, 4 figures. v2: references added and minor correction
F-Theorem without Supersymmetry
The conjectured F-theorem for three-dimensional field theories states that
the finite part of the free energy on S^3 decreases along RG trajectories and
is stationary at the fixed points. In previous work various successful tests of
this proposal were carried out for theories with {\cal N}=2 supersymmetry. In
this paper we perform more general tests that do not rely on supersymmetry. We
study perturbatively the RG flows produced by weakly relevant operators and
show that the free energy decreases monotonically. We also consider large N
field theories perturbed by relevant double trace operators, free massive field
theories, and some Chern-Simons gauge theories. In all cases the free energy in
the IR is smaller than in the UV, consistent with the F-theorem. We discuss
other odd-dimensional Euclidean theories on S^d and provide evidence that
(-1)^{(d-1)/2} \log |Z| decreases along RG flow; in the particular case d=1
this is the well-known g-theorem.Comment: 34 pages, 2 figures; v2 refs added, minor improvements; v3 refs
added, improved section 4.3; v4 minor improvement
Comments on Holographic Entanglement Entropy and RG Flows
Using holographic entanglement entropy for strip geometry, we construct a
candidate for a c-function in arbitrary dimensions. For holographic theories
dual to Einstein gravity, this c-function is shown to decrease monotonically
along RG flows. A sufficient condition required for this monotonic flow is that
the stress tensor of the matter fields driving the holographic RG flow must
satisfy the null energy condition over the holographic surface used to
calculate the entanglement entropy. In the case where the bulk theory is
described by Gauss-Bonnet gravity, the latter condition alone is not sufficient
to establish the monotonic flow of the c-function. We also observe that for
certain holographic RG flows, the entanglement entropy undergoes a 'phase
transition' as the size of the system grows and as a result, evolution of the
c-function may exhibit a discontinuous drop.Comment: References adde
Is Renormalized Entanglement Entropy Stationary at RG Fixed Points?
The renormalized entanglement entropy (REE) across a circle of radius R has
been proposed as a c-function in Poincar\'e invariant (2+1)-dimensional field
theory. A proof has been presented of its monotonic behavior as a function of
R, based on the strong subadditivity of entanglement entropy. However, this
proof does not directly establish stationarity of REE at conformal fixed points
of the renormalization group. In this note we study the REE for the free
massive scalar field theory near the UV fixed point described by a massless
scalar. Our numerical calculation indicates that the REE is not stationary at
the UV fixed point.Comment: 15 pages, 4 figure
Lagrangians for generalized Argyres-Douglas theories
We continue the study of Lagrangian descriptions of \mathcalN=2
Argyres-Douglas theories. We use our recent interpretation in terms of
sequential confinement to guess the Lagrangians of all the Argyres-Douglas
models with Abelian three dimensional mirror. We find classes of four
dimensional \mathcalN=1 quivers that flow in the infrared to generalized
Argyres-Douglas theories, such as the models. We study in
detail how the \mathcalN=1 chiral rings map to the Coulomb and Higgs
Branches of the \mathcalN=2 CFT's. The three dimensional mirror RG flows
are shown to land on the \mathcalN=4 complete graph quivers. We also
compactify to three dimensions the gauge theory dual to , and find
the expected Abelianization duality with \mathcalN=4 SQED with flavors
CD4+ T Cell Depletion, Immune Activation and Increased Production of Regulatory T Cells in the Thymus of HIV-Infected Individuals
Mechanisms by which HIV affects the thymus are multiple and only partially known, and the role of thymic dysfunction in HIV/AIDS immunopathogenesis remains poorly understood. To evaluate the effects of HIV infection on intra-thymic precursors of T cells in HIV-infected adults, we conducted a detailed immunophenotypic study of thymic tissue isolated from 7 HIV-infected and 10 HIV-negative adults who were to undergo heart surgery. We found that thymuses of HIV-infected individuals were characterized by a relative depletion of CD4+ single positive T cells and a corresponding enrichment of CD8+ single positive T cells. In addition, thymocytes derived from HIV-infected subjects showed increased levels of activated and proliferating cells. Our analysis also revealed a decreased expression of interleukin-7 receptor in early thymocytes from HIV-infected individuals, along with an increase in this same expression in mature double- and single-positive cells. Frequency of regulatory T cells (CD25+FoxP3+) was significantly increased in HIV-infected thymuses, particularly in priorly-committed CD4 single positive cells. Our data suggest that HIV infection is associated with a complex set of changes in the immunophenotype of thymocytes, including a reduction of intrathymic CD4+ T cell precursors, increased expression of activation markers, changes in the expression pattern of IL-7R and enrichment of T regulatory cells generation
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