What wire gauge should I use for a 15 amp half hot outlet?
A half hot receptacle, sometimes called a split switched receptacle, has one half controlled by a wall switch and the other half always energized. On a 15 ampere branch circuit the conductors are 14 AWG copper, which Table 310.16 rates at 20 amperes in the 60 degree C column and which 240.4(D)(3) restricts to a 15 ampere overcurrent device. Nothing about splitting a receptacle changes the conductor size. The circuit rating sets the wire.
What changes is the cable you pull to the box. You need 14/3 with ground from the switch to the receptacle so you have a switched hot on the red, a constant hot on the black, a shared neutral on the white, and the equipment grounding conductor. Break off the brass tab between the two hot terminals on the receptacle with lineman pliers. Leave the silver side tab intact so both halves share the neutral.
Do not break the neutral tab
Section 300.3(B) requires all conductors of the same circuit to be in the same raceway or cable, and 200.4 prohibits using a neutral for more than one branch circuit except where specifically permitted. Breaking the silver tab creates two separate neutral paths in one device, which is a common field mistake that leads to an open neutral on one half when a wire nut backs out. Break only the brass tab.
Where the NEC counts a half hot receptacle
Section 210.70(A)(1) requires at least one wall switch controlled lighting outlet in every habitable room and bathroom, and its exception 1 allows one or more receptacles controlled by a wall switch to serve in place of the lighting outlet in habitable rooms other than kitchens and bathrooms. That exception is the reason half hot receptacles exist in bedrooms and living rooms. The switched half stands in for a ceiling fixture.
Section 210.52(A) counts the receptacle as a required receptacle outlet for wall space spacing. A switched half does not disqualify it. What does matter is 406.3(E), which requires receptacles controlled by a wall switch to be marked or otherwise identified in some dwelling situations, and local practice usually satisfies that by controlling only the top half consistently throughout the house.
AFCI, GFCI, and tamper resistance
Section 210.12(A) requires AFCI protection for 120 volt, single phase, 15 and 20 ampere branch circuits supplying outlets in dwelling unit kitchens, family rooms, dining rooms, living rooms, parlors, libraries, dens, bedrooms, sunrooms, recreation rooms, closets, hallways, laundry areas, and similar rooms. A living room half hot falls squarely inside that list. Section 406.12 requires tamper resistant receptacles in those same dwelling areas.
If you are using a 20 ampere circuit instead, the conductor becomes 12 AWG copper and the receptacle must be a 20 ampere or 15 ampere device per Table 210.21(B)(3), which allows a 15 ampere receptacle on a 20 ampere circuit when two or more receptacles are on that circuit.
Field takeaway
14 AWG copper on a 15 ampere breaker, 14/3 cable from the switch box to the receptacle box, brass tab broken, silver tab left alone, AFCI protected, tamper resistant. Control the top half so the house is consistent.