Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userConformal invariance versus Weyl invariance
102
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The most general lagrangian describing spin 2 particles in flat spacetime and containing operators up to (mass) dimension 6 is carefully analyzed, determining the precise conditions for it to be invariant under linearized (transverse) diffeomorphisms, linearized Weyl rescalings, and conformal transformations.
rate research
Read More
There exists a certain argument that in even dimensions, scale invariant quantum field theories are conformal invariant. We may try to extend the argument in $2n + epsilon$ dimensions, but the naive extension has a small loophole, which indeed shows an obstruction in non-linear sigma models in $2+epsilon$ dimensions. Even though it could have failed due to the loophole, we show that scale invariance does imply conformal invariance of non-linear sigma models in $2+epsilon$ dimension from the seminal work by Perelman on the Ricci flow.
We propose a superspace formulation for the Weyl multiplet of N=1 conformal supergravity in five dimensions. The corresponding superspace constraints are invariant under super-Weyl transformations generated by a real scalar parameter. The minimal supergravity multiplet, which was introduced by Howe in 1981, emerges if one couples the Weyl multiplet to an Abelian vector multiplet and then breaks the super-Weyl invariance by imposing the gauge condition W=1, with W the field strength of the vector multiplet. The geometry of superspace is shown to allow the existence of a large family of off-shell supermultiplets that possess uniquely determined super-Weyl transformation laws and can be used to describe supersymmetric matter. Many of these supermultiplets have not appeared within the superconformal tensor calculus. We formulate a manifestly locally supersymmetric and super-Weyl invariant action principle. In the super-Weyl gauge W=1, this action reduces to that constructed in arXiv:0712.3102. We also present a superspace formulation for the dilaton Weyl multiplet.
In Lagrangian gauge systems, the vector space of global reducibility parameters forms a module under the Lie algebra of symmetries of the action. Since the classification of global reducibility parameters is generically easier than the classification of symmetries of the action, this fact can be used to constrain the latter when knowing the former. We apply this strategy and its generalization for the non-Lagrangian setting to the problem of conformal symmetry of various free higher spin gauge fields. This scheme allows one to show that, in terms of potentials, massless higher spin gauge fields in Minkowski space and partially-massless fields in (A)dS space are not conformal for spin strictly greater than one, while in terms of curvatures, maximal-depth partially-massless fields in four dimensions are also not conformal, unlike the closely related, but less constrained, maximal-depth Fradkin--Tseytlin fields.
For a class of $D=5$ holographic models we construct boomerang RG flow solutions that start in the UV at an $AdS_5$ vacuum and end up at the same vacuum in the IR. The RG flows are driven by deformations by relevant operators that explicitly break translation invariance. For specific models, such that they admit another $AdS_5$ solution, $AdS_5^c$, we show that for large enough deformations the RG flows approach an intermediate scaling regime with approximate conformal invariance governed by $AdS^c_5$. For these flows we calculate the holographic entanglement entropy and the entropic $c$-function for the RG flows. The latter is not monotonic, but it does encapsulate the degrees of freedom in each scaling region. For a different set of models, we find boomerang RG flows with intermediate scaling governed by an $AdS_2timesmathbb{R}^3$ solution which breaks translation invariance. Furthermore, for large enough deformations these models have interesting and novel thermal insulating ground states for which the entropy vanishes as the temperature goes to zero, but not as a power-law. Remarkably, the thermal diffusivity and the butterfly velocity for these new insulating ground states are related via $D=Ev^2_B/(2pi T)$, with $E(T)to 0.5$ as $Tto 0$.
In a recent work, it has been pointed out that certain observables of the massless scalar field theory in a static spherically symmetric background exhibit a universal behavior at large distances. More precisely, it was shown that, unlike what happens in the case the coupling to the curvature xi is generic, for the special cases xi=0 and xi = 1/6 the large distance behavior of the expectation value <T^{mu}_{ u}> turns out to be independent of the internal structure of the gravitational source. Here, we address a higher dimensional generalization of this result: We first compute the difference between a black hole and a static spherically symmetric star for the observables <phi^2> and <T^{mu}_{ u}> in the far field limit. Thus, we show that the conformally invariant massless scalar field theory in a static spherically symmetric background exhibits such universality phenomenon in Dgeq 4 dimensions. Also, using the one-loop effective action, we compute <T^{mu}_{ u}> for a weakly gravitating object. These results lead to the explicit expression of the expectation value <T^{mu}_{ u}> for a Schwarzschild-Tangherlini black hole in the far field limit. As an application, we obtain quantum corrections to the gravitational potential in D dimensions, which for D=4 are shown to agree with the one-loop correction to the graviton propagator previously found in the literature.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
