Universality and Clustering in 1+1 Dimensional Superstring-Bit Models

We construct a 1+1 dimensional superstring-bit model for D=3 Type IIB superstring. This low dimension model escapes the problems encountered in higher dimension models: (1) It possesses full Galilean supersymmetry; (2) For noninteracting polymers of bits, the exactly soluble linear superpotential describing bit interactions is in a large universality class of superpotentials which includes ones bounded at spatial infinity; (3) The latter are used to construct a superstring-bit model with the clustering properties needed to define an $S$-matrix for closed polymers of superstring-bits.Comment: 11 pages, Latex documen

Defining the Force between Separated Sources on a Light Front

The Newtonian character of gauge theories on a light front requires that the longitudinal momentum P^+, which plays the role of Newtonian mass, be conserved. This requirement conflicts with the standard definition of the force between two sources in terms of the minimal energy of quantum gauge fields in the presence of a quark and anti-quark pinned to points separated by a distance R. We propose that, on a light front, the force be defined by minimizing the energy of gauge fields in the presence of a quark and an anti-quark pinned to lines (1-branes) oriented in the longitudinal direction singled out by the light front and separated by a transverse distance R. Such sources will have a limited 1+1 dimensional dynamics. We study this proposal for weak coupling gauge theories by showing how it leads to the Coulomb force law. For QCD we also show how asymptotic freedom emerges by evaluating the S-matrix through one loop for the scattering of a particle in the N_c representation of color SU(N_c) on a 1-brane by a particle in the \bar N_c representation of color on a parallel 1-brane separated from the first by a distance R<<1/Lambda_{QCD}. Potential applications to the problem of confinement on a light front are discussed.Comment: LaTeX, 15 pages, 12 figures; minor typos corrected; numerical correction in equation 3.

Regularized Green's Function for the Inverse Square Potential

A Green's function approach is presented for the D-dimensional inverse square potential in quantum mechanics. This approach is implemented by the introduction of hyperspherical coordinates and the use of a real-space regulator in the regularized version of the model. The application of Sturm-Liouville theory yields a closed expression for the radial energy Green's function. Finally, the equivalence with a recent path-integral treatment of the same problem is explicitly shown.Comment: 10 pages. The final section was expande

Calculating the Rest Tension for a Polymer of String Bits

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint, UFIFT-HEP-94

Quantum Newtonian Dynamics on a Light Front

We recall the special features of quantum dynamics on a light-front (in an infinite momentum frame) in string and field theory. The reason this approach is more effective for string than for fields is stressed: the light-front dynamics for string is that of a true Newtonian many particle system, since a string bit has a fixed Newtonian mass. In contrast, each particle of a field theory has a variable Newtonian mass P^+, so the Newtonian analogy actually requires an infinite number of species of elementary Newtonian particles. This complication substantially weakens the value of the Newtonian analogy in applying light-front dynamics to nonperturbative problems. Motivated by the fact that conventional field theories can be obtained as infinite tension limits of string theories, we propose a way to recast field theory as a standard Newtonian system. We devise and analyze some simple quantum mechanical systems that display the essence of the proposal, and we discuss prospects for applying these ideas to large N_c QCD.Comment: 13 pages, 3 figures, LaTex, psfig, references added, APS copyrigh

String Spectrum of 1+1-Dimensional Large N QCD with Adjoint Matter

We propose gauging matrix models of string theory to eliminate unwanted non-singlet states. To this end we perform a discretised light-cone quantisation of large N gauge theory in 1+1 dimensions, with scalar or fermionic matter fields transforming in the adjoint representation of SU(N). The entire spectrum consists of bosonic and fermionic closed-string excitations, which are free as N tends to infinity. We analyze the general features of such bound states as a function of the cut-off and the gauge coupling, obtaining good convergence for the case of adjoint fermions. We discuss possible extensions of the model and the search for new non-critical string theories.Comment: 20 pages (7 figures available from authors as postscipt files), PUPT-134

Fine-Tuning Renormalization and Two-particle States in Nonrelativistic Four-fermion Model

Various exact solutions of two-particle eigenvalue problems for nonrelativistic contact four-fermion current-current interaction are obtained. Specifics of Goldstone mode is investigated. The connection between a renormalization procedure and construction of self-adjoint extensions is revealed.Comment: 13 pages, LaTex, no figures, to be published in IJMP

Longitudinal profiling of circulating tumour DNA for tracking tumour dynamics in pancreatic cancer.

BACKGROUND: The utility of circulating tumour DNA (ctDNA) for longitudinal tumour monitoring in pancreatic ductal adenocarcinoma (PDAC) has not been explored beyond mutations in the KRAS proto-oncogene. Here, we aimed to characterise and track patient-specific somatic ctDNA variants, to assess longitudinal changes in disease burden and explore the landscape of actionable alterations. METHODS: We followed 3 patients with resectable disease and 4 patients with unresectable disease, including 4 patients with ≥ 3 serial follow-up samples, of whom 2 were rare long survivors (> 5 years). We performed whole exome sequencing of tumour gDNA and plasma ctDNA (n = 20) collected over a ~ 2-year period from diagnosis through treatment to death or final follow-up. Plasma from 3 chronic pancreatitis cases was used as a comparison for analysis of ctDNA mutations. RESULTS: We detected > 55% concordance between somatic mutations in tumour tissues and matched serial plasma. Mutations in ctDNA were detected within known PDAC driver genes (KRAS, TP53, SMAD4, CDKN2A), in addition to patient-specific variants within alternative cancer drivers (NRAS, HRAS, MTOR, ERBB2, EGFR, PBRM1), with a trend towards higher overall mutation loads in advanced disease. ctDNA alterations with potential for therapeutic actionability were identified in all 7 patients, including DNA damage response (DDR) variants co-occurring with hypermutation signatures predictive of response to platinum chemotherapy. Longitudinal tracking in 4 patients with follow-up > 2 years demonstrated that ctDNA mutant allele fractions and clonal trends were consistent with CA19-9 measurements and/or clinically reported disease burden. The estimated prevalence of 'stem clones' was highest in an unresectable patient where changes in ctDNA dynamics preceded CA19-9 levels. Longitudinal evolutionary trajectories revealed ongoing subclonal evolution following chemotherapy. CONCLUSION: These results provide proof-of-concept for the use of exome sequencing of serial plasma to characterise patient-specific ctDNA profiles, and demonstrate the sensitivity of ctDNA in monitoring disease burden in PDAC even in unresectable cases without matched tumour genotyping. They reveal the value of tracking clonal evolution in serial ctDNA to monitor treatment response, establishing the potential of applied precision medicine to guide stratified care by identifying and evaluating actionable opportunities for intervention aimed at optimising patient outcomes for an otherwise intractable disease