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Topic: Closed string

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Open string

Type IIA string theory

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Superstring theory

String theory

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	What is string theory?
		In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.
		The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.
		String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions.
	superstringtheory.com /basics/basic4.html (436 words)

	String (physics) - Wikipedia, the free encyclopedia
		A string is an object with a one-dimensional spatial extent, unlike an elementary particle which is zero-dimensional.
		According to string theory, the various elementary particles in the standard model of quantum field theory correspond to different vibrational modes of tiny fundamental strings.
		However, the developments in string theory in the 1990s have shown that the open strings should always be thought of as ending on a new type of objects called the D-branes, and the spectrum of possibilities for open strings has increased greatly.
	en.wikipedia.org /wiki/Closed_string (383 words)

	Taking the Particle out of Particle Physics
		The simplest string is the relativistic string, whose mass and tension are described by a single parameter, reflecting the fact that the vibrations of the string propagate at the speed of light.
		The string theory which is presently having the most success in describing the particles and forces observed in nature is a closed string theory where the vibrations traveling counterclockwise around the string have no extra degrees of freedom, while the clockwise ones do.
		Although quantization of the particle is straightforward, consistency of the quantization of the string introduces a particularly unusual feature: The dimension of spacetime is determined to be 26 for the simplest string, and 10 or 2 for those with extra degrees of freedom.
	insti.physics.sunysb.edu /~siegel/quo.html (1777 words)

	string theory concept from the Astronomy knowledge base (Site not responding. Last check: 2007-11-06)
		Postulated to have formed as a result of processes in the early universe, cosmic strings are 1-dimensional structures of enormous energy, extending for perhaps thousands or millions of light years in space.
		String theory harmoniously unites quantum mechanics and general relativity the previously known laws of the small and the large, that are otherwise incompatible.
		closed string (2 facts) - A type of string that is in the shape of a loop.
	www.site.uottawa.ca:4321 /astronomy/stringtheory.html (636 words)

	String Theory
		Originally, string theory was proposed as an explanation for the observed relationship between mass and spin for certain particles called hadrons, which include the proton and neutron.
		But particles in string theory arise as excitations of the string, and included in the excitations of a string in string theory is a particle with zero mass and two units of spin.
		This led early string theorists to propose that string theory be applied not as a theory of hadronic particles, but as a theory of quantum gravity, the unfulfilled fantasy of theoretical physics in the particle and gravity communities for decades.
	members.tripod.com /oceanoz/string.html (1500 words)

	Is String Theory in Knots?
		The statistics of a whole loop of string would be the sum of the fractional statistics of its partons and would be an integer or half integer so that the string can live in three dimensional space.
		The 2 dimensional string world sheets and 3 dimensional space-time are more visible only because they stand out as a consequence of some as yet unknown quirk in the maths.
		The associative algebra is graded by parity of the length of strings.
	www.weburbia.com /pg/knots.htm (2891 words)

	SUPERSTRINGS! Supersymmetric Strings
		Open strings can carry gauge degrees of freedom at their endpoints, and cancellation of anomalies uniquely constrains the gauge group to be SO(32).
		The two gravitini (superpartners to the graviton) move in opposite directions on the closed string world sheet and have opposite chiralities under the 10 dimensional Lorentz group, so this is a non-chiral theory.
		This is a closed string theory with worldsheet fields moving in one direction on the world sheet which have a supersymmetry and fields moving in the opposite direction which have no supersymmetry.
	www.sukidog.com /jpierre/strings/susy.htm (695 words)

	Open string backgrounds from boundary state deformations \| The String Coffee Table (Site not responding. Last check: 2007-11-06)
		Therefore the open string disk correlator on the brane is physically the same as a closed string emission from the brane with a certain source term corresponding to the open string boundary condition.
		Of course the result is that the Wilson line over the closed string with which one acts on the boundary state of the bare brane has to come from a gauge field which satisfies the YM equations of motion.
		The only difference is that in the open string case the transformation is ‘cut in half’ (see here), which is the reson why it gives a genuinely new background, not just a gauge shift for the open string.
	golem.ph.utexas.edu /string/archives/000381.html (1932 words)

	3.1 The KLT relations in string theory
		The KLT relations between open and closed string theory amplitudes can be motivated by the observation that any closed string vertex operator for the emission of a closed string state (such as a graviton) is a product of open string vertex operators (see e.g.
		Indeed, the celebrated Koba-Nielsen form of string amplitudes [88], which may be obtained by evaluating correlations of the vertex operators, factorize at the level of the integrands before world sheet integrations are performed.
		Similarly, the four-point amplitudes corresponding to a heterotic closed superstring [75, 76] are
	relativity.livingreviews.org /Articles/lrr-2002-5/node7.html (608 words)

	MIT Physics Faculty: Barton Zwiebach
		His central contributions have been in the area of String Field Theory, where he did the early work on the construction of open string field theory and then developed the field theory of closed strings.
		In 1999, Ashoke Sen and Zwiebach showed that open string field theory can be used to calculate the tachyon potential and to confirm the existence of a critical point at the expected depth.
		The developments that followed led to vacuum string field theory, a new version of open string field theory based on the vacuum of the tachyon.
	web.mit.edu /physics/facultyandstaff/faculty/barton_zwiebach.html (382 words)

	Superstring Theory
		In the open string case, the left- and right-mover oscillator terms are not independent, having been linked by the boundary condition, and a separation into left and right movers is not particularly useful.
		It was found in the 1960s that the spin (or angular momentum) of a family of resonances (short-lived elementary particles) is related to the square of mass by a simple line on a graph, which is known as Regge trajectory.
		The idea is that as strings vibrate through the extra curled-up dimensions, the precise arrangement of the various holes and the way in which the Calabi-Yau shape folds around them has a direct impact on the possible resonant patterns of vibration.
	universe-review.ca /R15-18-string.htm (8226 words)

	String theory - Wikipedia, the free encyclopedia
		Bosonic string theories are 26-dimensional, while superstring and M-theories turn out to involve 10 or 11 dimensions.
		In this sense, string theory is still in a "larval stage": it is not a proper physical theory.
		Philosophically, string theory cannot be truly fundamental in its present formulation because it is background-dependent: each string theory is built on a fixed spacetime background.
	en.wikipedia.org /wiki/String_theory (6379 words)

	String Theory from Sample space
		This loop or closed string moving through time is also known as a world-sheet.
		The parameters used to close these events are the usual parameters of time found in the classical study of physical field theories.
		Yet, in each case you start with strings and end with strings, and the number of strings at the end need not be the same as what you started with.
	www.sirus.com /users/mjake/StringTh.html (2627 words)

	Lauda & Pfeiffer on Open-Closed Topological Strings \| The String Coffee Table (Site not responding. Last check: 2007-11-06)
		Furthermore there is an algebra homomorphism between the closed string sector and the center of the open string sector.
		These morphisms capture the action of worldsheets where a closed string splits into an open string (the ‘zipper’) and the reverse situation where an open string merges its ends to a closed string (the ‘co-zipper’).
		A closed Toplogical CFT (TCFT) is then a differential graded symmetric monoidal functor from this category to the categories of chain complexes (ie, dg-Vect, I think).
	golem.ph.utexas.edu /string/archives/000680.html (1796 words)

	Cosmology ... weakness of stringtheory
		Pelastration: So if a string is restructuring of the spacetime, meaning: a local coupling of two spots of Spacetime, you get a specific 'joined' zone of spacetime with a 'unique' vibration (which is different from the general vibration).
		We're not sure that string theory, or any theory, could provide answers to the beginning of the universe, but it's a goal that many of us are desperate to try to reach.
		And it turned out in string theory in the late '80s and early '90s we actually were able to calculate examples where you could really see changes in the topology of spacetime.
	www.mu6.com /stringtheory.html (3170 words)

	AntiGravity Propulsion - SuperStrings
		String theory is a science in progress; we are still learning new and unexpected things about it everyday.
		Whether or not string theory actually describes the universe that we live in is not known - yet.
		The string tension in string theory is denoted by the quantity 1/(2 pi a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.
	antigravitypower.tripod.com /SuperStrings (824 words)

	Closed string theory as a 3D adS QFT? (via CobWeb/3.1 planetlab2.isi.jhu.edu) (Site not responding. Last check: 2007-11-06)
		The universal cover of the conformal compactification of 2D Minkowski space has the topology S^1 x R, which is the same as the worldsheet topology of a closed string (at least, in it's original form).
		So, first quantized closed string theory using Polyakov variables in the conformal gauge is a 2D conformal field theory.
		Also, for open string theory, we can choose the gauge where h is the 2D adS metric (why not?) since the topology is right.
	www.lns.cornell.edu.cob-web.org:8888 /spr/2003-11/msg0056527.html (217 words)

	Amazon.ca: String Theory: Books: Joseph Polchinski (Site not responding. Last check: 2007-11-06)
		It then goes on to present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and fl hole entropy, and discusses many classic results in conformal field theory.
		The final four chapters are concerned with four-dimensional string theories, and have two goals: to show how some of the simplest string models connect with previous ideas for unifying the Standard Model; and to collect many important and beautiful general results on world-sheet and spacetime symmetries.
		In the second volume of the series the author generalizes the results of the first to string theories where supersymmetry is present.
	www.amazon.ca /String-Theory-Joseph-Polchinski/dp/0521672287 (1334 words)

	Luboš Motl's reference frame: Closed string vacuum solved analytically
		Around 1998, Ashoke Sen conjectured that the open string tachyon may get a vev that corresponds to a complete annihilation of the D-brane onto which the open strings were attached.
		Martin's work is a breakthrough in our understanding of cubic string field theory because it gives a complete, well-defined, and concrete solution for the single most important nontrivial classical configuration of the cubic open string field theory: the so-called closed string vacuum.
		Instead of the Siegel gauge that requires the string field to be annihilated by "b0", Martin demands it to be annihilated by the zero mode of the "b"-antighost calculated in a different coordinate system.
	motls.blogspot.com /2005/11/closed-string-vacuum-solved.html (794 words)

	Mode expansion for a closed string?
		I've had a browse through chapter 12 of Zweibach and, while he mentions the mode expansion for the closed string, he doesn't go through the derivation.
		The closed string case is actually easier than the open one.
		So contrary to the open string case left and right moving modes are independent of eachother.
	www.physicsforums.com /showthread.php?t=117379 (1510 words)

	Various String Theories
		Different string theories may employ different forms of strings for their basic building blocks.
		Three of the five string theories are superstring theories, that is, they combine string theory with supersymmetry.
		Closed strings have periodic boundary conditions, the string comes back on itself.
	ffden-2.phys.uaf.edu /212_fall2003.web.dir/erik_johnson/various.html (198 words)

	SUPERSTRINGS! D-branes (Site not responding. Last check: 2007-11-06)
		For example closed strings have periodic boundary conditions (the string comes back onto itself).
		This manifold is called a D-brane or Dp-brane ('p' is an integer which is the number of spatial dimensions of the manifold).
		Notice how the closed string becomes an open string with endpoints on the D-brane at the intermediate point in the interaction.
	www.physics.ucsb.edu /~strings/superstrings/dbranes.htm (324 words)

	closed string concept from the Astronomy knowledge base (Site not responding. Last check: 2007-11-06)
		closed string concept from the Astronomy knowledge base
		abstraction > hypothesis > theory > unified theory > string theory > closed string
		has definition A type of string that is in the shape of a loop.
	www.site.uottawa.ca:4321 /astronomy/closedstring.html (61 words)

	Rajesh Gopakumar (Site not responding. Last check: 2007-11-06)
		(an open topological string theory) with closed topological string theory on a space known as the resolved conifold.
		It is also a natural description of the second quantised closed strings and their intractions in the PP-wave background.
		Another example of the interplay between open and closed strings is in open string systems which possess tachyonic instabilities.
	www.mri.ernet.in /~annlrepo/node21.html (416 words)

	[No title]
		If the pattern is found the scanner advances past the input that matched and returns the string that matched the pattern.
		An invocation of this method of the form nextByte() behaves in exactly the same way as the invocation nextByte(radix), where radix is the default radix of this scanner.
		The string representation of a Scanner contains information that may be useful for debugging.
	faculty.washington.edu /stepp/scanner/Scanner.java (3142 words)

	SUPERSTRINGS! String Basics
		A generalization of this is fundamental strings which are 1-dimensional objects.
		These strings have certain vibrational modes which can be characterized by various quantum numbers such as mass, spin, etc. The basic idea is that each mode carries a set of quantum numbers that correspond to a distinct type of fundamental particle.
		In string theory, higher order diagrams correspond to the number of holes (or handles) in the world sheet.
	www.sukidog.com /jpierre/strings/basics.htm (584 words)

	CiteULike: Closed Bosonic String Field Theory at Quintic Order: Five-Tachyon Contact Term and Dilaton Theorem (Site not responding. Last check: 2007-11-06)
		We solve the geometry of the closed string field theory five-point vertex.
		Our solution is calculated in terms of quadratic Strebel differentials which are found numerically all over the relevant subspace of the moduli space of spheres with five punctures.
		This cancellation, achieved with a precision of about 0.1%, is within the estimated margin error on the contact term and is therefore a very good evidence that our computations are reliable.
	www.citeulike.org /user/mumrah/article/884594 (426 words)

	String Theory for Mathematicians (Site not responding. Last check: 2007-11-06)
		The author intends to compile them into an introductory string theory textbook for a mathematical audience, covering the massless spectrum of the five standard string theories and related topics.
		These notes are from a series of lectures given at Microsoft Research from August 1999 through March 2000 while the author was a Post Doctoral Researcher in the Theory Group.
		Second quantization, left- and right-movers, massless closed string spectrum, tachyons and gravitons.
	math.uoregon.edu /~greg/strings (319 words)

	Grig Software :: View topic - [closed] Minimum String to match (Site not responding. Last check: 2007-11-06)
		With RE you'll be able to define a match for a paragraph number, and make Compare It ignore all matching strings.
		Beware of this: In case the two strings do not have the same lenght you have to set the longer string in the R1-box and have it replaced with the shorter (R2-box).
		If I use the replace statement and make this string replace with a space (blank) and I set the option in the options-dialop tp ignore blanks it should filter out any smaller strings as defined.
	www.grigsoft.com /forum/viewtopic.php?p=999 (1305 words)

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