Introduction to Vacuum Technology

Vacuum systems are critical to many industries. They are vital to establishing required process pressures, establishing a clean process environment, and removing reaction by-products from the process chamber. This text, a revision and expansion of David Hata’s Introduction to Vacuum Technology published in 2008, addresses basic topics in vacuum technology for individuals tasked with maintaining vacuum systems and instructors teaching technician-level courses. The topics are carefully curated to the needs of technicians in a production environment and the types of vacuum systems used, and the accompanying laboratory manual and instructor’s guide support the delivery of lecture-laboratory courses. This book approaches vacuum systems from a pressure regime viewpoint, covering basic vacuum science, followed by the rough vacuum regime, including gas load, pumping mechanisms, pressure measurement, vacuum system construction, and basic troubleshooting concepts. The study of high vacuum systems follows and the same topics are revisited, and finally the topics of leak detection and residual gas analysis are discussed. Access all versions of this text and ancillaries at milneopentextbooks.org. Reader’s feedback via this survey would greatly help the authors to maintain and improve this book which was developed under National Science Foundation grant #2000454.https://knightscholar.geneseo.edu/oer-ost/1033/thumbnail.jp

B field and squeezed states in Vacuum String Field Theory

We show that squeezed state solutions for solitonic lumps in Vacuum String Field Theory still exist in the presence of a constant B field. We show in particular that, just as in the B=0 case, we can write down a compact explicit form for such solutions.Comment: 15 pages, Latex, typos corrected, final versio

Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models

We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest $c=0$ case, we derive the explicit forms of the Hamiltonians for the higher critical case $k=3$ (which corresponds to $c=-22/5$) and for the case $c=1/2$, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and $W_3$ algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.Comment: 70 pages, LaTeX, typographical errors are corrected, to be published in Phys. Rev.

Dressed Sliver solutions in Vacuum String Field Theory

We consider a new class of solutions (dressed slivers) in Vacuum String Field Theory, which represent D25-branes. For each dressed sliver we introduce a deformation parameter and define a family of states which are characterized by new abelian star-subalgebras. We show that this deformation parameter can be used as a regulator: it allows us to define for each such solution a finite norm and energy density. Finally we show how to generalize these results to parallel coincident and to lower dimensional branes.Comment: 39 pages, JHEP style. v2:minor corrections, references adde

Construction of the Vacuum String Field Theory on a non-BPS Brane

In the framework of the Sen conjectures a construction of vacuum superstring field theory on a non-BPS brane is discussed. A distinguished feature of this theory is a presence of a ghost kinetic operator mixing GSO+/- sectors. A candidate for such kinetic operator with zero cohomology is discussed.Comment: expression for the pure ghost kinetic operator corrected, Comments added; 21 pages, 1 figure, LaTeX 2

Star Algebra Projectors

Surface states are open string field configurations which arise from Riemann surfaces with a boundary and form a subalgebra of the star algebra. We find that a general class of star algebra projectors arise from surface states where the open string midpoint reaches the boundary of the surface. The projector property of the state and the split nature of its wave-functional arise because of a nontrivial feature of conformal maps of nearly degenerate surfaces. Moreover, all such projectors are invariant under constant and opposite translations of their half-strings. We show that the half-string states associated to these projectors are themselves surface states. In addition to the sliver, we identify other interesting projectors. These include a butterfly state, which is the tensor product of half-string vacua, and a nothing state, where the Riemann surface collapses.Comment: 65 pages, 23 figures, LaTe

Ratio of Tensions from Vacuum String Field Theory

We show analytically that the ratio of the norm of sliver states agrees with the ratio of D-brane tensions. We find that the correct ratio appears as a twist anomaly.Comment: 13 pages, lanlmac; version to appear in JHE

Stringy NJL and Gross-Neveu models at finite density and temperature

Nonlocal stringy versions of the Nambu-Jona-Lasinio and Gross-Neveu models arise in a certain limit of holographic QCD. We analyze the phase structure at finite density and temperature at strong coupling in terms of probe branes in the gravity dual. Comparison with the phase structure of the local field theory models shows qualitative agreement with some aspects, and disagreement with others. Finally, we explain how to construct the Landau potentials for these models by taking the probe branes off-shell.Comment: 32 pages, uses JHEP3.cls; v2, references added, version to be submitted to JHE

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Experimental String Field Theory

We develop efficient algorithms for level-truncation computations in open bosonic string field theory. We determine the classical action in the universal subspace to level (18,54) and apply this knowledge to numerical evaluations of the tachyon condensate string field. We obtain two main sets of results. First, we directly compute the solutions up to level L=18 by extremizing the level-truncated action. Second, we obtain predictions for the solutions for L > 18 from an extrapolation to higher levels of the functional form of the tachyon effective action. We find that the energy of the stable vacuum overshoots -1 (in units of the brane tension) at L=14, reaches a minimum E_min = -1.00063 at L ~ 28 and approaches with spectacular accuracy the predicted answer of -1 as L -> infinity. Our data are entirely consistent with the recent perturbative analysis of Taylor and strongly support the idea that level-truncation is a convergent approximation scheme. We also check systematically that our numerical solution, which obeys the Siegel gauge condition, actually satisfies the full gauge-invariant equations of motion. Finally we investigate the presence of analytic patterns in the coefficients of the tachyon string field, which we are able to reliably estimate in the L -> infinity limit.Comment: 37 pages, 6 figure