String (physics)

In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities.^[1] Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity.^{[citation needed]}

Overview

In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties.^[2] Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry (these five are known as superstring theories) and two versions without supersymmetry known as bosonic string theories, which differed in the type of strings and in other aspects. Today, these different superstring theories are thought to arise as different limiting cases of a single theory called M-theory.

In string theories of particle physics, the strings are very tiny; much smaller than can be observed in today's particle accelerators. The characteristic length scale of strings is typically on the order of the Planck length, about 10⁻³⁵ meter, the scale at which the effects of quantum gravity are believed to become significant. Therefore on much larger length scales, such as the scales visible in physics laboratories, such entities would appear to be zero-dimensional point particles. Strings are able to vibrate as harmonic oscillators, and different vibrational states of the same string are interpreted as different types of particles. In string theories, strings vibrating at different frequencies constitute the multiple fundamental particles found in the current Standard Model of particle physics. Strings are also sometimes studied in nuclear physics where they are used to model flux tubes.

As the string propagates through spacetime, a string sweeps out a two-dimensional surface called its worldsheet. This is analogous to the one-dimensional worldline traced out by a point particle. The physics of a string is described by means of a two-dimensional conformal field theory associated with the worldsheet. The formalism of two-dimensional conformal field theory also has many applications outside of string theory, for example in condensed matter physics and parts of pure mathematics.

Types of strings

Closed and open strings

Strings can be either open or closed. A closed string is a string that has no end-points, and therefore is topologically equivalent to a circle. An open string, on the other hand, has two end-points and is topologically equivalent to a line interval. Not all string theories contain open strings, but every theory must contain closed strings, as interactions between open strings can always result in closed strings.

The oldest superstring theory containing open strings was type I string theory. 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 physical degree of freedom called D-branes, and the spectrum of possibilities for open strings has significantly increased.

Open and closed strings are generally associated with characteristic vibrational modes. One of the vibration modes of a closed string can be identified as the graviton. In certain string theories, the lowest-energy vibration of an open string is a tachyon and can undergo tachyon condensation. Other vibrational modes of open strings exhibit the properties of photons and gluons.

Orientation

Strings can also possess an orientation, which can be thought of as an internal "arrow" that distinguishes the string from one with the opposite orientation. By contrast, an unoriented string is one with no such arrow on it.

References

^ Becker, Katrin; Schwarz, John H.; Becker, Melanie (2007). String theory and M-theory: a modern introduction. Cambridge New York: Cambridge University Press. p. 6. ISBN 978-0-511-25653-0.
^ Polchinski, Joseph Gerard (2004). String theory. Vol. 1: An introduction to the bosonic string / Joseph Polchinski (Reprint ed.). Cambridge: Cambridge Univ. Press. ISBN 978-0521633031.

Schwarz, John (2000). "Introduction to Superstring Theory". Retrieved Dec. 12, 2005.
"NOVA's strings homepage"

[1] Becker, Katrin; Schwarz, John H.; Becker, Melanie (2007). String theory and M-theory: a modern introduction. Cambridge New York: Cambridge University Press. p. 6. ISBN 978-0-511-25653-0.

[polchinski1-2] Polchinski, Joseph Gerard (2004). String theory. Vol. 1: An introduction to the bosonic string / Joseph Polchinski (Reprint ed.). Cambridge: Cambridge Univ. Press. ISBN 978-0521633031.

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v t e String theory
Background	Strings Cosmic strings History of string theory First superstring revolution Second superstring revolution String theory landscape
Theory	Nambu–Goto action Polyakov action Bosonic string theory Superstring theory Type I string Type II string Type IIA string Type IIB string Heterotic string N=2 superstring F-theory String field theory Matrix string theory Non-critical string theory Non-linear sigma model Tachyon condensation RNS formalism GS formalism
String duality	T-duality S-duality U-duality Montonen–Olive duality
Particles and fields	Graviton Dilaton Tachyon Ramond–Ramond field Kalb–Ramond field Magnetic monopole Dual graviton Dual photon
Branes	D-brane NS5-brane M2-brane M5-brane S-brane Black brane Black holes Black string Brane cosmology Quiver diagram Hanany–Witten transition
Conformal field theory	Virasoro algebra Mirror symmetry Conformal anomaly Conformal algebra Superconformal algebra Vertex operator algebra Loop algebra Kac–Moody algebra Wess–Zumino–Witten model
Gauge theory	Anomalies Instantons Chern–Simons form Bogomol'nyi–Prasad–Sommerfield bound Exceptional Lie groups (G₂, F₄, E₆, E₇, E₈) ADE classification Dirac string p-form electrodynamics
Geometry	Worldsheet Kaluza–Klein theory Compactification Why 10 dimensions? Kähler manifold Ricci-flat manifold Calabi–Yau manifold Hyperkähler manifold K3 surface G₂ manifold Spin(7)-manifold Generalized complex manifold Orbifold Conifold Orientifold Moduli space Hořava–Witten theory K-theory (physics) Twisted K-theory
Supersymmetry	Supergravity Eleven-dimensional supergravity Type I supergravity Type IIA supergravity Type IIB supergravity Superspace Lie superalgebra Lie supergroup
Holography	Holographic principle AdS/CFT correspondence
M-theory	Matrix theory Introduction to M-theory
String theorists	Aganagić Arkani-Hamed Atiyah Banks Berenstein Bousso Curtright Dijkgraaf Distler Douglas Duff Dvali Ferrara Fischler Friedan Gates Gliozzi Gopakumar Green Greene Gross Gubser Gukov Guth Hanson Harvey 't Hooft Hořava Gibbons Kachru Kaku Kallosh Kaluza Kapustin Klebanov Knizhnik Kontsevich Klein Linde Maldacena Mandelstam Marolf Martinec Minwalla Moore Motl Mukhi Myers Nanopoulos Năstase Nekrasov Neveu Nielsen van Nieuwenhuizen Novikov Olive Ooguri Ovrut Polchinski Polyakov Rajaraman Ramond Randall Randjbar-Daemi Roček Rohm Sagnotti Scherk Schwarz Seiberg Sen Shenker Siegel Silverstein Sơn Staudacher Steinhardt Strominger Sundrum Susskind Townsend Trivedi Turok Vafa Veneziano Verlinde Verlinde Wess Witten Yau Yoneya Zamolodchikov Zamolodchikov Zaslow Zumino Zwiebach