Hanany-Witten transition
Encyclopedia
In theoretical physics
the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory
in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten
in their 1996 paper Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities
and T-dualities
.
. They considered a configuration of NS5-brane
s, D5-branes
and D3-branes which today is called a Hanany–Witten brane cartoon. They demonstrated that a subsector of the corresponding open string theory is described by a 3-dimensional Yang–Mills gauge theory. However they found that the string theory space of solutions, called the moduli space
, only agreed with the known Yang-Mills moduli space if whenever an NS5-brane and a D5-brane cross, a D3-brane stretched between them is created or destroyed.
They also presented various other arguments in support of their effect, such as a derivation from the worldvolume Wess–Zumino terms. This proof uses the fact that the flux from each brane renders the action
of the other brane ill-defined if one does not include the D3-brane.
configuration the number of D3-branes stretched between a D5-brane and an NS5-brane may only be equal to 0 or 1. Then the Hanany-Witten effect implies that after the D5-brane and the NS5-brane cross, if there was a single D3-brane stretched between them it will be destroyed, and if there was not one then one will be created.
.
one finds that when two M5-branes cross, one creates or destroys an M2-brane. Using S-duality one may obtain transitions without NS5-brane. For example, when a D5-brane and a D3-cross one creates or destroys a fundamental string.
Theoretical physics
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physics to rationalize, explain and predict natural phenomena...
the Hanany–Witten transition, also called the Hanany–Witten effect, refers to any process in a superstring theory
Superstring theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modelling them as vibrations of tiny supersymmetric strings...
in which two p-branes cross resulting in the creation or destruction of a third p-brane. A special case of this process was first discovered by Amihay Hanany and Edward Witten
Edward Witten
Edward Witten is an American theoretical physicist with a focus on mathematical physics who is currently a professor of Mathematical Physics at the Institute for Advanced Study....
in their 1996 paper Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics. All other known cases of Hanany–Witten transitions are related to the original case via combinations of S-dualities
S-duality
In theoretical physics, S-duality is an equivalence of two quantum field theories or string theories. An S-duality transformation maps states and vacua with coupling constant g in one theory to states and vacua with coupling constant 1/g in the dual theory...
and T-dualities
T-duality
T-duality is a symmetry of quantum field theories with differing classical descriptions, of which the relationship between small and large distances in various string theories is a special case. Discussion of the subject originated in a paper by T. S. Buscher and was further developed by Martin...
.
The original effect
The original Hanany–Witten transition was discovered in type IIB superstring theory in flat, 10-dimensional Minkowski spaceMinkowski space
In physics and mathematics, Minkowski space or Minkowski spacetime is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated...
. They considered a configuration of NS5-brane
NS5-brane
In theoretical physics, the NS5-brane is a five-dimensional object in string theory that carries a magnetic charge under the B-field, the field under which the fundamental string is electrically charged....
s, D5-branes
D-brane
In string theory, D-branes are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes were discovered by Dai, Leigh and Polchinski, and independently by Hořava in 1989...
and D3-branes which today is called a Hanany–Witten brane cartoon. They demonstrated that a subsector of the corresponding open string theory is described by a 3-dimensional Yang–Mills gauge theory. However they found that the string theory space of solutions, called the moduli space
Moduli space
In algebraic geometry, a moduli space is a geometric space whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects...
, only agreed with the known Yang-Mills moduli space if whenever an NS5-brane and a D5-brane cross, a D3-brane stretched between them is created or destroyed.
They also presented various other arguments in support of their effect, such as a derivation from the worldvolume Wess–Zumino terms. This proof uses the fact that the flux from each brane renders the action
Action (physics)
In physics, action is an attribute of the dynamics of a physical system. It is a mathematical functional which takes the trajectory, also called path or history, of the system as its argument and has a real number as its result. Action has the dimension of energy × time, and its unit is...
of the other brane ill-defined if one does not include the D3-brane.
The S-rule
Furthermore they discovered the S-rule, which states that in a supersymmetricSupersymmetry
In particle physics, supersymmetry is a symmetry that relates elementary particles of one spin to other particles that differ by half a unit of spin and are known as superpartners...
configuration the number of D3-branes stretched between a D5-brane and an NS5-brane may only be equal to 0 or 1. Then the Hanany-Witten effect implies that after the D5-brane and the NS5-brane cross, if there was a single D3-brane stretched between them it will be destroyed, and if there was not one then one will be created.
(p,q) 5-branes
More generally, NS5-branes and D5-branes may form bound states known as (p,q) 5-branes. The above argument was extended in Branes and Supersymmetry Breaking in Three Dimensional Gauge Theories to the case of a (p,q) and a (p',q') 5-brane which cross. The authors found that the number of D3-branes created or destroyed must be equal to pq'-p'q. Furthmore they showed that this leads to a generalized S-rule, which states that in a supersymmetric configuration the number of D3-branes never goes negative upon crossing two 5-branes. If it does go negative, then the gauge theory exhibits spontaneous supersymmetry breakingSpontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
.
Dual forms of the effect
Via a series of T-dualities one obtains the result that in any type II superstring theory, when an NS5-brane and a Dp-brane cross one necessarily creates of destroys a D(p-2)-brane. Lifting this statement to M-theoryM-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...
one finds that when two M5-branes cross, one creates or destroys an M2-brane. Using S-duality one may obtain transitions without NS5-brane. For example, when a D5-brane and a D3-cross one creates or destroys a fundamental string.