In the context of quantum field theory (QFT), the UV/IR fixed point refers to a special property of certain theories where the behavior in the ultraviolet (UV) and infrared (IR) regions of the theory becomes linked or related.
To understand this concept, let's first define the UV and IR regimes. The UV regime refers to high-energy or short-distance scales, where quantum effects dominate and the theory is sensitive to small-scale structures. On the other hand, the IR regime refers to low-energy or long-distance scales, where classical or macroscopic behavior emerges.
In some QFTs, particularly those with conformal symmetry or scale invariance, there can exist a fixed point where the theory's behavior remains the same under a change in scale. This means that the theory exhibits the same physics at all energy scales, from the UV to the IR.
The UV/IR fixed point specifically refers to a situation where the behavior of a QFT in the UV regime becomes directly related to its behavior in the IR regime. In other words, properties of the theory at high energies can provide information about its behavior at low energies, and vice versa.
This fixed point is often associated with a phenomenon called holography or the gauge/gravity duality. The holographic principle suggests that a quantum field theory in a certain number of dimensions can be mathematically described by a gravitational theory in one higher dimension. In this context, the UV/IR fixed point can be understood as a consequence of the correspondence between the high-energy regime of the QFT and the gravitational physics in the higher-dimensional spacetime.
The UV/IR fixed point has been extensively studied in the context of gauge/gravity duality, particularly in the framework of string theory and its dual gravitational descriptions. It has provided valuable insights into the relationship between quantum field theories and gravity, shedding light on various aspects of strongly coupled systems, such as the behavior of quark-gluon plasmas and condensed matter systems.
It's worth noting that the UV/IR fixed point is a concept that arises in specific theories and frameworks, and its general applicability to all QFTs is still an area of ongoing research.