Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userAspects of CFTs on Real Projective Space
104
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present an analytic study of conformal field theories on the real projective space $mathbb{RP}^d$, focusing on the two-point functions of scalar operators. Due to the partially broken conformal symmetry, these are non-trivial functions of a conformal cross ratio and are constrained to obey a crossing equation. After reviewing basic facts about the structure of correlators on $mathbb{RP}^d$, we study a simple holographic setup which captures the essential features of boundary correlators on $mathbb{RP}^d$. The analysis is based on calculations of Witten diagrams on the quotient space $AdS_{d+1}/mathbb{Z}_2$, and leads to an analytic approach to two-point functions. In particular, we argue that the structure of the conformal block decomposition of the exchange Witten diagrams suggests a natural basis of analytic functionals, whose action on the conformal blocks turns the crossing equation into certain sum rules. We test this approach in the canonical example of $phi^4$ theory in dimension $d=4-epsilon$, extracting the CFT data to order $epsilon^2$. We also check our results by standard field theory methods, both in the large $N$ and $epsilon$ expansions. Finally, we briefly discuss the relation of our analysis to the problem of construction of local bulk operators in AdS/CFT.
rate research
Read More
Harmonic maps that minimise the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge three lumps is a $7$-dimensional manifold of cohomogeneity one which can be described as a one-parameter family of symmetry orbits of $D_2$ symmetric maps. In this paper, we discuss the charge three moduli spaces of lumps from two perspectives: discrete symmetries of lumps and the Riemann-Hurwitz formula. We then calculate the metric and find explicit formulas for various geometric quantities. We also discuss the implications for lump decay.
We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanishes when the conformal dimension and spin are those of a double twist operator $Delta = 2Delta_phi + ell + 2n$. By analytically continuing to Lorentzian signature we show that the spectral density at high spatial momenta has support on the spectrum condition $|omega| > |k|$. This leads to a series of sum rules. Finally, we explicitly match the thermal block expansion with the momentum space Greens function at finite temperature in several examples.
We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm, we dramatically improve previous bounds on a number of CFT quantities, particularly for theories with global symmetries. In the case of SO(4) or SU(2) symmetry, our bounds severely constrain models of conformal technicolor. In N=1 superconformal theories, we place strong bounds on dim(Phi*Phi), where Phi is a chiral operator. These bounds asymptote to the line dim(Phi*Phi) <= 2 dim(Phi) near dim(Phi) ~ 1, forbidding positive anomalous dimensions in this region. We also place novel upper and lower bounds on OPE coefficients of protected operators in the Phi x Phi OPE. Finally, we find examples of lower bounds on central charges and flavor current two-point functions that scale with the size of global symmetry representations. In the case of N=1 theories with an SU(N) flavor symmetry, our bounds on current two-point functions lie within an O(1) factor of the values realized in supersymmetric QCD in the conformal window.
A local SL(2,Z) transformation on the Type IIB brane configuration gives rise to an interesting class of superconformal field theories, known as the S-fold CFTs. Previously it has been proposed that the corresponding quiver theory has a link involving the T(U(N)) theory. In this paper, we generalise the preceding result by studying quivers that contain a T(G) link, where G is self-dual under S-duality. In particular, the cases of G = SO(2N), USp(2N) and G_2 are examined in detail. We propose the theories that arise from an appropriate insertion of an S-fold into a brane system, in the presence of an orientifold threeplane or an orientifold fiveplane. By analysing the moduli spaces, we test such a proposal against its S-dual configuration using mirror symmetry. The case of G_2 corresponds to a novel class of quivers, whose brane construction is not available. We present several mirror pairs, containing G_2 gauge groups, that have not been discussed before in the literature.
We use holography in order to study the entropy of thermal CFTs on (1+1)-dimensional curved backgrounds that contain horizons. Starting from the metric of the BTZ black hole, we perform explicit coordinate transformations that set the boundary metric in de Sitter or black-hole form. For a de Sitter boundary, the dual picture describes a CFT at a temperature different from that of the cosmological horizon. We determine minimal surfaces that allow us to compute the entanglement entropy of a boundary region, as well as the temperature affecting the energy associated with a probe quark on the boundary. For an entangling surface that coincides with the horizon, we study the relation between entanglement and gravitational entropy through an appropriate definition of the effective Newtons constant. We find that the leading contribution to the entropy is proportional to the horizon area, with a coefficient that accounts for the degrees of freedom of a CFT thermalized above the horizon temperature. We demonstrate the universality of our findings by considering the most general metric in a (2+1)-dimensional AdS bulk containing a non-rotating black hole and a static boundary with horizons.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
