STOCK MARKET SIMULATION

Using tools and information available from the Internet, a five-week stock market simulation was performed to understand the different effects of short-term trading and long-term trading strategies. The total profits gained by the two methods were compared to determine which method was more effective for stock investment. The experience of this project could lead to a better comprehension of the stock market and will be helpful for actual stock market investment in the future

(2,2) Superconformal Bootstrap in Two Dimensions

We find a simple relation between two-dimensional BPS N=2 superconformal blocks and bosonic Virasoro conformal blocks, which allows us to analyze the crossing equations for BPS 4-point functions in unitary (2,2) superconformal theories numerically with semidefinite programming. We constrain gaps in the non-BPS spectrum through the operator product expansion of BPS operators, in ways that depend on the moduli of exactly marginal deformations through chiral ring coefficients. In some cases, our bounds on the spectral gaps are observed to be saturated by free theories, by N=2 Liouville theory, and by certain Landau-Ginzburg models.Comment: 56 pages, 14 figure

On Higher Derivative Couplings in Theories with Sixteen Supersymmetries

We give simple arguments for new non-renormalization theorems on higher derivative couplings of gauge theories to supergravity, with sixteen supersymmetries, by considerations of brane-bulk superamplitudes. This leads to some exact results on the effective coupling of D3-branes in type IIB string theory. We also derive exact results on higher dimensional operators in the torus compactification of the six dimensional (0, 2) superconformal theory.Comment: 31 pages, 10 figures, section 2 reconstructured, new result in section 3.2, additional clarifications adde

Supersymmetry Constraints and String Theory on K3

We study supervertices in six dimensional (2,0) supergravity theories, and derive supersymmetry non-renormalization conditions on the 4- and 6-derivative four-point couplings of tensor multiplets. As an application, we obtain exact non-perturbative results of such effective couplings in type IIB string theory compactified on K3 surface, extending previous work on type II/heterotic duality. The weak coupling limit thereof, in particular, gives certain integrated four-point functions of half-BPS operators in the nonlinear sigma model on K3 surface, that depend nontrivially on the moduli, and capture worldsheet instanton contributions.Comment: 47 pages, 4 figure

Little String Amplitudes (and the Unreasonable Effectiveness of 6D SYM)

We study tree level scattering amplitudes of four massless states in the double scaled little string theory, and compare them to perturbative loop amplitudes in six-dimensional super-Yang-Mills theory. The little string amplitudes are computed from correlators in the cigar coset CFT and in N=2 minimal models. The results are expressed in terms of integrals of conformal blocks and evaluated numerically in the alpha' expansion. We find striking agreements with up to 2-loop scattering amplitudes of massless gluons in 6D SU(k) SYM at a Z_k invariant point on the Coulomb branch. We comment on the issue of UV divergence at higher loop orders in the gauge theory and discuss the implication of our results.Comment: 58 pages, 5 figures, 3 tables, comments added, references adde

Topological Defect Lines and Renormalization Group Flows in Two Dimensions

We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion categories without braiding. We study the crossing relations of TDLs, discuss their relation to the 't Hooft anomaly, and use them to constrain renormalization group flows to either conformal critical points or topological quantum field theories (TQFTs). We show that if certain non-invertible TDLs are preserved along a RG flow, then the vacuum cannot be a non-degenerate gapped state. For various massive flows, we determine the infrared TQFTs completely from the consideration of TDLs together with modular invariance.Comment: 101 pages, 63 figures, 2 tables; v3: minor changes, added footnotes and references, published versio

Twist Gap and Global Symmetry in Two Dimensions

We show that every compact, unitary two-dimensional conformal field theory with an Abelian conserved current has vanishing twist gap for charged primary fields with respect to the u(1)×Virasoro algebra. This means that either the chiral algebra is enhanced by a charged primary field with zero twist or there is an infinite family of charged primary fields that accumulate to zero twist