21 research outputs found
Surface defects in the model
I study the two-dimensional defects of the dimensional critical
model and the defect RG flows between them. By combining the
-expansion around and as well as large
techniques, I find new conformal defects and examine their behavior across
dimensions and at various . I discuss how some of these fixed points relate
to the known ordinary, special and extraordinary transitions in the 3d theory,
as well as examine the presence of new symmetry breaking fixed points
preserving an subgroup of for (with the
estimate ). I characterise these fixed points by obtaining their
conformal anomaly coefficients, their 1-point functions and comment on the
calculation of their string potential. These results establish surface
operators as a viable approach to the characterisation of interface critical
phenomena in the 3d critical model. They also suggest the existence of a
vaster array of surface defects yet to be discovered.Comment: 19 pages, 2 figures; v2: added reference
BPS surface operators and calibrations
We present here a careful study of the holographic duals of BPS surface
operators in the 6d theory. Several different classes of
surface operators have been recently identified and each class has a specific
calibration form - a 3-form in whose pullback to the M2-brane
world-volume is equal to the volume form. In all but one class, the appropriate
forms are closed, so the action of the M2-brane is easily expressed in terms of
boundary data, which is the geometry of the surface. Specifically, for surfaces
of vanishing anomaly, it is proportional to the integral of the square of the
extrinsic curvature. This can be extended to the case of surfaces with
anomalies, by taking the ratio of two surfaces with the same anomaly. This
gives a slew of new expectation values at large in this theory.
For one specific class of surface operators, which are Lagrangian
submanifolds of , the structure is far
richer and we find that the M2-branes are special Lagrangian submanifold of an
appropriate six-dimensional almost Calabi-Yau submanifold of .
This allows for an elegant treatment of many such examples.Comment: 15 page
Bootstrapping string dynamics in the 6d theories
We present two complementary approaches to calculating the 2-point function
of stress tensors in the presence of a 1/2 BPS surface defect of the 6d
theories. First, we use analytical bootstrap techniques
at large to obtain the first nontrivial correction to this correlator, from
which we extract the defect CFT (dCFT) data characterising the 2d dCFT of the
1/2 BPS plane. Along the way we derive a supersymmetric inversion formula,
obtain the relevant superconformal blocks and check that crossing symmetry is
satisfied. Notably our result features a holomorphic function whose appearance
is related to the chiral algebra construction of Beem, Rastelli and van Rees.
Second, we use that chiral algebra description to obtain exact results for the
BPS sector of the dCFT, valid at any and for any choice of surface
operator. These results provide a window into the dynamics of strings of the
mysterious 6d theories.Comment: 32 pages, 3 figure
Defect CFT techniques in the 6d theory
Surface operators are among the most important observables of the 6d
theory. Here we apply the tools of defect CFT to study
local operator insertions into the 1/2-BPS plane. We first relate the 2-point
function of the displacement operator to the expectation value of the bulk
stress tensor and translate this relation into a constraint on the anomaly
coefficients associated with the defect. Secondly, we study the defect operator
expansion of the stress tensor multiplet and identify several new operators of
the defect CFT. Technical results derived along the way include the explicit
supersymmetry tranformations of the stress tensor multiplet and the
classification of unitary representations of the superconformal algebra
preserved by the defect.Comment: 41 pages, two figure
Quantum holographic surface anomalies
Expectation values of surface operators suffer from logarithmic divergences
reflecting a conformal anomaly. In a holographic setting, where surface
operators can be computed by a minimal surface in , the leading
contribution to the anomaly comes from a divergence in the classical action (or
area) of the minimal surface. We study the subleading correction to it due to
quantum fluctuations of the minimal surface. In the same way that the
divergence in the area does not require a global solution but only a
near-boundary analysis, the same holds for the quantum corrections. We study
the asymptotic form of the fluctuation determinant and show how to use the heat
kernel to calculate the quantum anomaly. In the case of M2-branes describing
surface operators in the theory in 6d, our calculation of the
one-loop determinant reproduces expressions for the anomaly that have been
found by less direct methods.Comment: 18 page
Quantum holographic surface anomalies
Expectation values of surface operators suffer from logarithmic divergences reflecting a conformal anomaly. In a holographic setting, where surface operators can be computed by a minimal surface in AdS, the leading contribution to the anomaly comes from a divergence in the classical action (or area) of the minimal surface. We study the subleading correction to it due to quantum fluctuations of the minimal surface. In the same way that the divergence in the area does not require a global solution but only a near-boundary analysis, the same holds for the quantum corrections. We study the asymptotic form of the fluctuation determinant and show how to use the heat kernel to calculate the quantum anomaly. In the case of M2-branes describing surface operators in the N=(2,0) theory in 6d, our calculation of the one-loop determinant reproduces expressions for the anomaly that have been found by less direct methods
Stabilité du vide
Un des problèmes fondamentaux qui survient dans la formulation de la théorie quantique des champs dans l’espace de Sitter est la transition possible vers l’espace Anti-de Sitter. Par un calcul semi-classique, on peut calculer le taux de transition, qui est non-nul. Or, une comparaison des degrés de liberté suggèrent qu’ils sont incompatibles et que la transition ne devrait pas avoir lieu. Une analyse plus approfondie d’un modèle de stabilité du vide met en lumière deux conditions qui pourraient résoudre ce paradoxe. En appliquant ces conditions au modèle standard, on obtient une borne sur la masse du boson de Higgs ainsi que sur la constante cosmologique. Bien qu’elles n’offrent pas une résolution complète du problème de la hiérarchie et de la constante cosmologique, ces contraintes pourraient jouer un rôle dans la formulation d’une théorie de la gravité quantique.A fundamental issue regarding the formulation of a consistent quantum de Sitter space theory is the possible transition to Anti-de Sitter space. Indeed, a semiclassical computation gives a nonzero estimate for the transition probability, while a counting of the degrees of freedom for both spaces shows their incompatilibity, leading to the expectation that the transition is impossible. Through a deeper analysis of quantum tunneling in a semiclassical theory including gravity, one can outline two consistency conditions that could alleviate this seemingly paradoxical disparity. Applying these consistency conditions to the Standard Model shed a different light on the hierarchy problem and the cosmological constant problem, although it does not solve them altogether. Nevertheless, they could play a role in the formulation of a consistent theory of quantum gravity