Boundary states in the SU(2)k_k WZW model from open string field theory

We analyze boundary states in the SU(2)$_k$ WZW model using open string field theory in the level truncation approximation. We develop algorithms that allow effective calculation of action in this model and we search for classical solutions of the equations of motion, which are conjectured to describe boundary states. We find three types of solutions. First, there are real solutions that represent maximally symmetric Cardy boundary states and we show that they satisfy certain selection rules regarding their SU(2) parameters. Next, we find complex solutions that go beyond the SU(2) model and describe maximally symmetric SL(2,$\mathbb C$) boundary conditions. Finally, we find exotic solutions that correspond to symmetry-breaking boundary states. Most of real exotic solutions describe the so-called B-brane boundary states, but some may represent yet unknown boundary states.Comment: v2: 95 pages, 6 figures, improved analysis of some solution

Černé díry v teorii strun

M. Guica, T. Hartman, W. Song a A. Strominger nedávno ukázali, že entropii extrémní Kerrovy černé díry lze vypočítat pomocí duality mezi kvantovou gravitací na pozadí černé díry a konformní teorií pole poblíž horizontu. V naší diplomové práci jsme nalezli zobecnění této procedury: opouštíme "near horizon" geometrii a definujeme okrajové podmínky a povrchové náboje v plném prostoročase na horizontu černé díry, kde takž "žije" duální konformní teorie pole. Pomocí této procedury znovu odvozujeme entropii extrémních černých děr a poté počítáme entropii obecných rotujících černých děr.Recently it was shown by M. Guica, T. Hartman, W. Song and A. Strominger that the entropy of extreme Kerr black hole can be computed through a duality between the quantum gravity on the background of the Kerr black hole and the conformal field theory near the horizon. In our diploma work we have found a generalization of this procedure: we leave the near horizon geometry and we define our boundary conditions and the surface charges in the full spacetime on the horizon of the black hole, where the dual conformal field theory "lives". We use this procedure to rederive the entropy of extremal black holes and then we compute the entropy of general rotating black holes.Institute of Theoretical PhysicsÚstav teoretické fyzikyFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Boundary State from Ellwood Invariants

Boundary states are given by appropriate linear combinations of Ishibashi states. Starting from any OSFT solution and assuming Ellwood conjecture we show that every coefficient of such a linear combination is given by an Ellwood invariant, computed in a slightly modified theory where it does not trivially vanish by the on-shell condition. Unlike the previous construction of Kiermaier, Okawa and Zwiebach, ours is linear in the string field, it is manifestly gauge invariant and it is also suitable for solutions known only numerically. The correct boundary state is readily reproduced in the case of known analytic solutions and, as an example, we compute the energy momentum tensor of the rolling tachyon from the generalized invariants of the corresponding solution. We also compute the energy density profile of Siegel-gauge multiple lump solutions and show that, as the level increases, it correctly approaches a sum of delta functions. This provides a gauge invariant way of computing the separations between the lower dimensional D-branes.Comment: v2: 63 pages, 14 figures. Major improvements in section 2. Version published in JHE

Transfer Learning on Structural Brain Age Models to Decode Cognition in MS: A Federated Learning Approach.

Introduction. Classical deep learning research requires lots of centralised data. However, data sets are often stored at different clinical centers, and sharing sensitive patient data such as brain images is difficult. In this manuscript, we investigated the feasibility of federated learning, sending models to the data instead of the other way round, for research on brain magnetic resonant images of people with multiple sclerosis (MS). Methods. Using transfer learning on a previously published brain age model, we trained a model to decode performance on the symbol digit modalities test (SDMT) of patients with MS from structural T1 weighted MRI. Three international centers in Brussels, Greifswald and Prague participated in the project. In Brussels, one computer served as the server coordinating the FL project, while the other served as client for model training on local data (n=97). The other two clients were Greifswald (n=104) and Prague (n=100). Each FL round, the server sent a global model to the clients, where its fully connected layer was updated on the local data. After collecting the local models, the server applied a weighted average of two randomly picked clients, yielding a new global model. Results. After 22 federated learning rounds, the average validation loss across clients reached a minimum. The model appeared to have learned to assign SDMT values close to the mean with a mean absolute error of 9.04, 10.59 and 10.71 points between true and predicted SDMT on the test data sets of Brussels, Greifswald and Prague respectively. The overall test MAE across all clients was 10.13 points. Conclusion. Federated learning is feasible for machine learning research on brain MRI of persons with MS, setting the stage for larger transfer learning studies to investigate the utility of brain age latent representations in cognitive decoding tasks

Black-hole solutions of Einstein equations in higher dimensions

Ústav teoretické fyzikyInstitute of Theoretical PhysicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Black holes in string theory

Recently it was shown by M. Guica, T. Hartman, W. Song and A. Strominger that the entropy of extreme Kerr black hole can be computed through a duality between the quantum gravity on the background of the Kerr black hole and the conformal field theory near the horizon. In our diploma work we have found a generalization of this procedure: we leave the near horizon geometry and we define our boundary conditions and the surface charges in the full spacetime on the horizon of the black hole, where the dual conformal field theory "lives". We use this procedure to rederive the entropy of extremal black holes and then we compute the entropy of general rotating black holes