15273018
Testing closed string field theory with marginal fields
We study the feasibility of level expansion and test the quartic vertex of closed string field theory by checking the flatness of the potential in marginal directions. The tests, which work out correctly, require the cancellation of two contributions: one from an infinite-level computation with the cubic vertex and the other from a finite-level computation with the quartic vertex. The numerical results suggest that the quartic vertex contributions are comparable or smaller than those of level four fields.
55601550
Fermion's Tunnelling with Effects of Quantum Gravity
In this paper, using Hamilton-Jacobi method, we address the tunnelling of fermions in a 4-dimensional Schwarzschild spacetime. Based on the generalized uncertainty principle, we introduce 
the influence of quantum gravity. After solving the equation of motion of the spin-1/2 field, we 
derive the corrected Hawking temperature. It turns out that the correction depends not only on 
the black hole’s mass but also on the mass (energy) of emitted fermions. It is of interest that, in 
our calculation, the quantum gravity correction decelerates the temperature increase during the radiation 
explicitly. This observation then naturally leads to the remnants in black hole evaporation. 
Our calculation shows that the residue mass is , where is the Planck mass and is a dimensionless parameter accounting for quantum gravity effects. The evaporation singularity is 
then avoided.
17081750
String Field Theory and Tachyon Dynamics
In this thesis we present some works done during my doctoral studies. These results focus on two directions. The first one is motivated by tachyon dynamics in open string theory. We calculate the stress tensors for the p-adic string model and for the pure tachyonic sector of open string field theory (OSFT). We give the energy density of lump solutions and attempt to evaluate the evolution of the pressure in rolling tachyon solutions. We discuss the relevance of the pressure calculation for the identification of the large time solution with a gas of closed strings. In the second direction, we give some results in closed string field theory (CSFT). We considered marginal deformations in CSFT. The marginal parameter, called a, is that associated with the dimension-zero primary operator cWcX&X. We use this marginal operator to test the quartic structure of CSFT and the feasibility of level expansion. We check the vanishing of the effective potential for a. In the level expansion the quartic terms generated by the cubic interactions must be cancelled by the elementary quartic interaction of four marginal operators. We confirm this prediction, thus giving evidence that the sign, normalization, and region of integration Vo, 4 for the quartic vertex are all correct. This is the first calculation of an elementary quartic amplitude for which there is an expectation that can be checked. We also extend the calculation to the case of the four marginal operators associated with two space coordinates. We then try to search a critical point of the tachyon potential in CSFT. We include the tachyon, the dilaton, and massive fields in the computation. Some evidence is found for the existence of a closed string tachyon vacuum. It seems that this critical point becomes more shallow when higher level contributions are considered. We also relate fields in the sigma model and those in CSFT. Moreover, large dilaton deformations are studied numerically. Finally, we use the low-energy effective field equations that couple gravity, the dilaton, and the bulk closed string tachyon to study the end result of the physical decay process associated with the instability of closed string tachyon. We establish that whenever the tachyon induces the rolling process, the Einstein metric undergoes collapse while the dilaton rolls to strong coupling. Some more general potentials and the possible cosmological application are discussed. Thesis Supervisor: Barton Zwiebach Title: Professor of Physics
118539816
Superluminal Neutrinos and Monopoles
In this letter, we show that superluminal neutrinos announced by OPERA could be explained by the existence of a monopole, which is left behind after the spontaneous symmetry breaking (SSB) phase transition of some scalar fields in the universe. We assume the 't Hooft-Polyakov monopole couples to the neutrinos but not photon fields. The monopole introduces a different effective metric to the neutrinos from the one experienced by photons. We find that the superluminal propagation only exists in a very short distance from the monopole, about $10^3$ cm in OPERA. No matter how far they travel, neutrinos always arrive earlier than photons by the same amount of time, provided a monopole existing on or close to their trajectories. This conclusion can be tested by future experiments. The result reconciles the contradiction between OPERA and supernova neutrinos. We further exclude cosmic strings as a possible theoretical explanation.
1154617
Stress Tensors in p-adic String Theory and Truncated OSFT
We construct the stress tensors for the p-adic string model and for the pure tachyonic sector of open string field theory by naive metric covariantization of the action. Then we give the concrete energy density of a lump solution of the p-adic model. In the cubic open bosonic string field theory, we also give the energy density of a lump solution and pressure evolution of a rolling tachyon solution.
55495910
Homogeneous Field and WKB Approximation in Deformed Quantum Mechanics with Minimal Length
In the framework of the deformed quantum mechanics with a minimal length, we consider the motion of a nonrelativistic particle in a homogeneous external field. We find the integral representation for the physically acceptable wave function in the position representation. Using the method of steepest descent, we obtain the asymptotic expansions of the wave function at large positive and negative arguments. We then employ the leading asymptotic expressions to derive the WKB connection formula, which proceeds from classically forbidden region to classically allowed one through a turning point. By the WKB connection formula, we prove the Bohr-Sommerfeld quantization rule up to . We also show that if the slope of the potential at a turning point is too steep, the WKB connection formula is no longer valid around the turning point. The effects of the minimal length on the classical motions are investigated using the Hamilton-Jacobi method. We also use the Bohr-Sommerfeld quantization to study statistical physics in deformed spaces with the minimal length.
18014891
Twisted bundles on noncommutative T4 and D-brane bound states
We construct twisted quantum bundles and adjoint sections on noncommutative $T^4$, and investigate relevant D-brane bound states with non-Abelian backgrounds. We also show that the noncommutative $T^4$ with non-Abelian backgrounds exhibits SO$(4,4|Z)$ duality and via this duality we get a Morita equivalent $T^4$ on which only D0-branes exist. For a reducible non-Abelian background, the moduli space of D-brane bound states in Type II string theory takes the form $\prod_a (T^4)^{q_a}/S_{q_a}$.
11205361
The CP(n) model on noncommutative plane
We construct the consistent CP(n) model on noncommutative plane. The Bogomolny bound on the energy is saturated by (anti-)self-dual solitons with integer topological charge, which is independent of their scaling and orientation. This integer quantization is satisfied for our general solutions, which turns out regular everywhere. We discuss the possible implication of our result to the instanton physics in Yang–Mills theories on noncommutative R4.
17983245
Boosted decision trees, a powerful event classifier
Consider the problem of classification of events between signal and background, given a number of particle identification (PID) variables. A decision tree is a sequence of binary splits of the data. To train the tree a set of known training events are used. The results are measured using a separate set of known testing events. Consider all of the data to be on one node. The best PID variable and best place on that variable to split the data into separate signal and background is found. There are then two nodes. The process is repeated on these new nodes and is continued until a given number of final nodes (called “leaves”) are obtained, or until all leaves are pure or until a node has too few events. There are several popular criteria to determine the best PID variable and best place on which to split a node. The gini criterion is used here. Suppose that event i has weight Wi. The purity P of a node is defined as the weight of signal events on the node divided by the total weight of events on that node. For a given node: gini = P (1 − P ) ∑ i Wi. gini is zero for P = 1 or P = 0. The best split is chosen as the one which minimizes gini. The next node to split is chosen by finding that node whose splitting maximizes the change in gini. In this way a decision tree is built. Leaves with P ≥ 0.5 are signal leaves and the rest are background leaves. Decision trees are powerful, but unstable. A small change in the training data can produce a large change in the tree. This is remedied by the use of boosting. For boosting, the training events which were misclassified (a signal event fell on a background leaf or vice versa) have their weights increased (boosted), and a new tree is formed. This procedure is then repeated for the new tree. In this way many trees are built up. The score from the mth individual tree Tm is taken as +1 if the event falls on a signal leaf and −1 if the event falls on a background leaf. The final score is taken as a weighted sum of the scores of the individual leaves. Two methods for boosting are considered here. The first is called AdaBoost. Define errm = weight misclassified/total weight for tree m. Let αm = β log [(1 − errm)/errm], where β is a constant. In the statistical literature β has been taken as one, but for the MiniBooNE experiment, β = 0.5 has been found to be the optimum value. The misclassified events have their weight multiplied by em . The weights are then renormalized so the sum of all of the training event weights is one. The final score is T = ∑Ntree m=1 αmTm. The second method of boosting considered here is called -boost or, sometimes, shrinkage. Misclassified events have their weight multiplied by e , where is a constant. For the MiniBooNE experiment, = 0.03 has been optimum. (The results vary only mildly as β or are changed a bit.) The final score is T = ∑Ntree m=1 Tm. -boost changes weights a little at a time, while AdaBoost can be shown to try to optimize each change in weights to minimize e where T is the score and y is +1 for a signal event and −1 for a background event. The optimum value is F = log prob/(1 − prob), where prob is the probability that y = 1, given the observed PID variables. In practice, for MiniBooNE, the two boosting methods have performed almost equally well. Boosting is described as using many weak classifiers to build a strong classifier. This is seen in Figure 1. After the first few trees, the misclassification fraction for an individual tree is above 40%. In the MiniBooNE experiment some hundreds of possible PID variables have been suggested. The most powerful of these have been selected by accepting those which are used most often as the splitting variable. Some care needs to be taken as some-
17770397
Noncommutative Spacetime and Emergent Gravity
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix model or a large N field theory where NC fields can be regarded as master fields of large N matrices. (II) NC fields essentially define vector (tetrad) fields. So they define a gravitational metric of some manifold as an emergent geometry from NC gauge fields. Of course, the pictures (I) and (II) should refer to the same physics, which should be familiar with the large N duality in string theory. The 1/N corrections in the picture (I) correspond to the derivative corrections in terms of the noncommutativity \theta for the picture (II).
14757513
On The Correspondence Between Noncommuative Field Theory And Gravity
In this brief review, we summarize the new development on the correspondence between noncommutative (NC) field theory and gravity, shortly referred to as the NCFT/Gravity correspondence. We elucidate why a gauge theory in NC spacetime should be a theory of gravity. A basic reason for the NCFT/Gravity correspondence is that the Λ-symmetry (or B-field transformations) in NC spacetime can be considered as a par with diffeomorphisms, which results from the Darboux theorem. This fact leads to a striking picture about gravity: Gravity can emerge from a gauge theory in NC spacetime. Gravity is then a collective phenomenon emerging from gauge fields living in fuzzy spacetime.