Spinning Strings and Integrable Spin Chains in the AdS/CFT Correspondence Jan Plefka
... limit. By now, these scaling dimensions have been firmly reproduced up to the three-loop order in gauge theory [21, 12, 53]. This has also led to important structural information for higher (or all-loop) attempts in gauge theory, which maximally employ the uncovered integrable structures to be discu ...
... limit. By now, these scaling dimensions have been firmly reproduced up to the three-loop order in gauge theory [21, 12, 53]. This has also led to important structural information for higher (or all-loop) attempts in gauge theory, which maximally employ the uncovered integrable structures to be discu ...
AdS/CFT Course Notes - Johns Hopkins University
... A natural question: what if we have a theory that does not change when we zoom out? This would be a scale invariant theory. In the case of high energy physics, where we have Poincaré symmetry, scale invariant theories are basically always conformally invariant QFTs,3 which are called Conformal Fiel ...
... A natural question: what if we have a theory that does not change when we zoom out? This would be a scale invariant theory. In the case of high energy physics, where we have Poincaré symmetry, scale invariant theories are basically always conformally invariant QFTs,3 which are called Conformal Fiel ...
Entanglement Entropy of non-Unitary Quantum Field Theory
... system is critical and we expect to be able to extract the central charge c of the critical point. What happens if |ψi is the ground state of a critical system described by a non-unitary CFT? We find that we may just replace c → ceff = c − 24∆. Here ceff is the effective central charge and ∆ is the ...
... system is critical and we expect to be able to extract the central charge c of the critical point. What happens if |ψi is the ground state of a critical system described by a non-unitary CFT? We find that we may just replace c → ceff = c − 24∆. Here ceff is the effective central charge and ∆ is the ...
Physics in Higher-Dimensional Manifolds
... 3-dimensional space (Tegmark 1997). Yet despite the preponderance of common sense to the contrary, many people have been interested in the idea that the world is a fundamentally higher-dimensional arena. Over the years such a notion has acquired an eclectic legion of followers; including everyone fr ...
... 3-dimensional space (Tegmark 1997). Yet despite the preponderance of common sense to the contrary, many people have been interested in the idea that the world is a fundamentally higher-dimensional arena. Over the years such a notion has acquired an eclectic legion of followers; including everyone fr ...
Constructible Regular n-gons
... integer, thus 2 is not invertible. The only invertible elements are 1 and −1. A field can have the cancellation property which states that if ab = ac then b = c. If a field has such a property it is called an integral domain. In other words an integral domain has no zero divisors, which are non-zero ...
... integer, thus 2 is not invertible. The only invertible elements are 1 and −1. A field can have the cancellation property which states that if ab = ac then b = c. If a field has such a property it is called an integral domain. In other words an integral domain has no zero divisors, which are non-zero ...
Proof and Computation in Geometry
... (in 1926) his theories of geometry using only one sort of variables, for points. The fundamental relations to be mentioned in geometry are usually (at least for the past 120 years) taken to be betweenness and equidistance. We write B(a, b, c) for “a, b, and c are collinear, and b is strictly between ...
... (in 1926) his theories of geometry using only one sort of variables, for points. The fundamental relations to be mentioned in geometry are usually (at least for the past 120 years) taken to be betweenness and equidistance. We write B(a, b, c) for “a, b, and c are collinear, and b is strictly between ...
Non-linear field theory with supersymmetry
... gravity with the help of supersymmetry have not materialized in a field theory context, they do describe the low-energy regime of superstring theories which are candidates for a quantum gravity theory. The Standard model model (SM) of elementary particle physics is the most successful physical theor ...
... gravity with the help of supersymmetry have not materialized in a field theory context, they do describe the low-energy regime of superstring theories which are candidates for a quantum gravity theory. The Standard model model (SM) of elementary particle physics is the most successful physical theor ...
Smooth Scaling of Valence Electronic Properties in Fullerenes: From
... The linear fits that define the icosahedral and nonicosahedral capacitance scaling lines both are very strong, as seen from the large values of R2 for each displayed in Fig. 1. Additionally, it is seen there that the icosahedral and nonicosahedral scaling lines nearly intersect at the C60 point. Thi ...
... The linear fits that define the icosahedral and nonicosahedral capacitance scaling lines both are very strong, as seen from the large values of R2 for each displayed in Fig. 1. Additionally, it is seen there that the icosahedral and nonicosahedral scaling lines nearly intersect at the C60 point. Thi ...
fractal geometry : an introduction
... self-similar, meaning thereby that a fractal is exactly or approximately similar to a part of itself. Self-similarity fractal is based on some equation which undergoes iteration. The length of a coastline measured with different length rulers may be an example of fractal. The shorter the ruler, the ...
... self-similar, meaning thereby that a fractal is exactly or approximately similar to a part of itself. Self-similarity fractal is based on some equation which undergoes iteration. The length of a coastline measured with different length rulers may be an example of fractal. The shorter the ruler, the ...
conformai, geometry - International Mathematical Union
... Conformai geometry, that is the study of those properties of geometric configurations which are invariant under all conformai transformations, has therefore not yet been developed into a systematic theory, comparable, for example, with projective geometry. The former theory is naturally more difficu ...
... Conformai geometry, that is the study of those properties of geometric configurations which are invariant under all conformai transformations, has therefore not yet been developed into a systematic theory, comparable, for example, with projective geometry. The former theory is naturally more difficu ...
BUSSTEPP Lectures on String Theory
... The main references for string theory used during the course were the standard books on the subject [31, 47] and the more recent review article [37]. The prerequisite supersymmetry lectures can be found in [20].1 The lectures were delivered in the morning and exercises were assigned for the tutorial ...
... The main references for string theory used during the course were the standard books on the subject [31, 47] and the more recent review article [37]. The prerequisite supersymmetry lectures can be found in [20].1 The lectures were delivered in the morning and exercises were assigned for the tutorial ...
Worked Homework Examples
... a. The side lengths should be twice as long. (This is because we used a 2 band stretcher. If we used a 3 band stretcher the image lengths would be three times as long. Students may not realize that it is because the distances from the image to the anchor point are all twice as long as the correspond ...
... a. The side lengths should be twice as long. (This is because we used a 2 band stretcher. If we used a 3 band stretcher the image lengths would be three times as long. Students may not realize that it is because the distances from the image to the anchor point are all twice as long as the correspond ...
Scale invariance
In physics, mathematics, statistics, and economics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor. The technical term for this transformation is a dilatation (also known as dilation), and the dilatations can also form part of a larger conformal symmetry.In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilatations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity.In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale.In quantum field theory, scale invariance has an interpretation in terms of particle physics. In a scale-invariant theory, the strength of particle interactions does not depend on the energy of the particles involved.In statistical mechanics, scale invariance is a feature of phase transitions. The key observation is that near a phase transition or critical point, fluctuations occur at all length scales, and thus one should look for an explicitly scale-invariant theory to describe the phenomena. Such theories are scale-invariant statistical field theories, and are formally very similar to scale-invariant quantum field theories.Universality is the observation that widely different microscopic systems can display the same behaviour at a phase transition. Thus phase transitions in many different systems may be described by the same underlying scale-invariant theory.In general, dimensionless quantities are scale invariant. The analogous concept in statistics are standardized moments, which are scale invariant statistics of a variable, while the unstandardized moments are not.