Bergman Kernel from Path Integral

We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kahler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.Comment: 27 page

Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge

We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the ones in the $ISO(3)$ Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave-function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, a partition function of each of these theories is expressed as an inner product of such wave-functions. Since the isomorphism preserves the inner products, the partition function of the two theories are the same for any closed orientable manifold. We also discuss on a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory.Comment: 32 pages + 20 figure

On the quantum mechanics of M(atrix) theory

We present a study of M(atrix) theory from a purely canonical viewpoint. In particular, we identify free particle asymptotic states of the model corresponding to the supergraviton multiplet of eleven dimensional supergravity. These states have a natural interpretation as excitations in the flat directions of the matrix model potential. Furthermore, we provide the split of the matrix model Hamiltonian into a free part describing the free propagation of these particle states along with the interaction Hamiltonian describing their interactions. Elementary quantum mechanical perturbation theory then yields an effective potential for these particles as an expansion in their inverse separation. Remarkably we find that the leading velocity independent terms of the effective potential cancel in agreement with the fact that there is no force between stationary D0 branes. The scheme we present provides a framework in which one can perturbatively compute the M(atrix) theory result for the eleven dimensional supergraviton S matrix.Comment: 28 pages, Latex2

Equations of motion, Noncommutativity and Quantization

We study the relation between a given set of equations of motion in configuration space and a Poisson bracket. A Poisson structure is consistent with the equations of motion if the symplectic form satisfy some consistency conditions. When the symplectic structure is commutative these conditions are the Helmholtz integrability equations for the nonrestricted inverse problem of the calculus of variations. We have found the corresponding consistency conditions for the symplectic noncommutative case.Comment: 18 pages, to appear PL

Low energy dynamics from deformed conformal symmetry in quantum 4D N = 2 SCFTs

We determine the one-loop deformation of the conformal symmetry of a general N}=2 superconformally invariant Yang-Mills theory. The deformation is computed for several explicit examples which have a realization as world-volume theories on a stack of D3 branes. These include (i) N=4 SYM with gauge groups SU(N), USp(2N) and SO(N); (ii) USp(2N) gauge theory with one hypermultiplet in the traceless antisymmetric representation and four hypermultiplets in the fundamental; (iii) quiver gauge theory with gauge group SU(N)xSU(N) and two hypermultiplets in the bifundamental representations (N,\bar N) and (bar N,N). The existence of quantum corrections to the conformal transformations imposes restrictions on the effective action which we study on a subset of the Coulomb branch corresponding to the separation of one brane from the stack. In the N=4 case, the one-loop corrected transformations provide a realization of the conformal algebra; this deformation is shown to be one-loop exact. For the other two models, higher-loop corrections are necessary to close the algebra. Requiring closure, we infer the two-loop conformal deformation.Comment: 30 pages, 0 figure

Outcomes of submucosal (T1b) esophageal adenocarcinomas removed by endoscopic mucosal resection

AIM: To investigate the outcomes and recurrences of pT1b esophageal adenocarcinoma (EAC) following endoscopic mucosal resection (EMR) and associated treatments. METHODS: Patients undergoing EMR with pathologically confirmed T1b EAC at two academic referral centers were retrospectively identified. Patients were divided into 4 groups based on treatment following EMR: Endoscopic therapy alone (group A), endoscopic therapy with either chemotherapy, radiation or both (group B), surgical resection (group C) or no further treatment/lost to follow-up (< 12 mo) (group D). Pathology specimens were reviewed by a central pathologist. Follow-up data was obtained from the academic centers, primary care physicians and/or referring physicians. Univariate analysis was performed to identify factors predicting recurrence of EAC. RESULTS: Fifty-three patients with T1b EAC underwent EMR, of which 32 (60%) had adequate follow-up ≥ 12 mo (median 34 mo, range 12-103). There were 16 patients in group A, 9 in group B, 7 in group C and 21 in group D. Median follow-up in groups A to C was 34 mo (range 12-103). Recurrent EAC developed overall in 9 patients (28%) including 6 (38%) in group A (median: 21 mo, range: 6-73), 1 (11%) in group B (median: 30 mo, range: 30-30) and 2 (29%) in group C (median 21 mo, range: 7-35. Six of 9 recurrences were local; of the 6 recurrences, 5 were treated with endoscopy alone. No predictors of recurrence of EAC were identified. CONCLUSION: Endoscopic therapy of T1b EAC may be a reasonable strategy for a subset of patients including those either refusing or medically unfit for esophagectomy

Generalized Niederer’s transformation for quantum Pais–Uhlenbeck oscillator

We extend, to the quantum domain, the results obtained in [Nucl. Phys. B 885 (2014) 150] and [Phys. Lett. B 738 (2014) 405] concerning Niederer’s transformation for the Pais–Uhlenbeck oscillator. Namely, the quantum counterpart (an unitary operator) of the transformation which maps the free higher derivatives theory into the Pais–Uhlenbeck oscillator is constructed. Some consequences of this transformation are discussed.The author is grateful to Joanna and Cezary Gonera, Piotr Kosiński and Paweł Maślanka for useful comments and remarks. The research was supported by the grant of National Science Center number DEC-2013/09/B/ST2/02205. Funded by SCOAP3

Cosmological Landscape From Nothing: Some Like It Hot

We suggest a novel picture of the quantum Universe -- its creation is described by the {\em density matrix} defined by the Euclidean path integral. This yields an ensemble of universes -- a cosmological landscape -- in a mixed state which is shown to be dynamically more preferable than the pure quantum state of the Hartle-Hawking type. The latter is dynamically suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum fields within the cosmological bootstrap (the self-consistent back reaction of hot matter). This bootstrap suggests a solution to the problem of boundedness of the on-shell cosmological action and eliminates the infrared catastrophe of small cosmological constant in Euclidean quantum gravity. The cosmological landscape turns out to be limited to a bounded range of the cosmological constant $\Lambda_{\rm min}\leq \Lambda \leq \Lambda_{\rm max}$. The domain $\Lambda<\Lambda_{\rm min}$ is ruled out by the back reaction effect which we analyze by solving effective Euclidean equations of motion. The upper cutoff is enforced by the quantum effects of vacuum energy and the conformal anomaly mediated by a special ghost-avoidance renormalization of the effective action. They establish a new quantum scale $\Lambda_{\rm max}$ which is determined by the coefficient of the topological Gauss-Bonnet term in the conformal anomaly. This scale is realized as the upper bound -- the limiting point of an infinite sequence of garland-type instantons which constitute the full cosmological landscape. The dependence of the cosmological constant range on particle phenomenology suggests a possible dynamical selection mechanism for the landscape of string vacua.Comment: Final version, to appear in JCA

Perturbative Gauge Theory As A String Theory In Twistor Space

Perturbative scattering amplitudes in Yang-Mills theory have many unexpected properties, such as holomorphy of the maximally helicity violating amplitudes. To interpret these results, we Fourier transform the scattering amplitudes from momentum space to twistor space, and argue that the transformed amplitudes are supported on certain holomorphic curves. This in turn is apparently a consequence of an equivalence between the perturbative expansion of ${\cal N}=4$ super Yang-Mills theory and the $D$-instanton expansion of a certain string theory, namely the topological $B$ model whose target space is the Calabi-Yau supermanifold $\Bbb{CP}^{3|4}$.Comment: 97 p